Help in Transition from Software engineer job to Teaching Job

You can go for a teaching job now. There are many degree colleges in private colleges where they will take MBAs for teaching for BA and B.Com students in the corresponding subjects.
In your question, you mentioned that you did your MBA. But you have not mentioned you have done your graduation in which subject.
To go for a teaching job in private colleges you need not get qualified in the NET examination. But the payment offered will be less. If you want to get a lecturer post in a government college with UGC scale you have to get qualified in the NET examination. Presently a candidate with PhD qualification need not get qualified in NET. But from the next year or so the UGC thinking of making NET compulsory to PhDs also. So you should keep this point in view.
Another way of entering into teaching job is to get qualified in B.Ed. B. Ed is a 2 years course. This course is offered in distance mode also. If you get enrolled now and complete your B.Ed you will get teacher post in government or private schools.

UGC-NET exam is conducted twice a year. Clear this exam to work as an assistant professor in college.
After clearing this exam you can apply for lecturer post in any college that is recognized by UGC.
Whenever you see a vacancy, you can apply there. You may need to go for a walk-in-interview. You may have to appear for written test as well as an interview.

Educational qualification required-
A master's degree in any subject with at least 55% in that subject- For general category candidates
A master's degree in any subject with at least 50% in that subject- For SC, ST, OBC, Transgender

You have some different and great idea after corporate experience in Software firm. You can try to apply for a Teacher or Professor jobs in any institute first. Your MBA is reasonably enough to apply for the same. There are many Assistant or Associate Professor vacancies in institutes available across.

You can refer the Jobs section of this site itself where you will come across the latest Teaching / Professor / Lecturer job vacancies across the nation posts. Collect the detail from there and apply it on-time.

Once you get the call for, try to attend the interview and show or demonstrate them your interest on teaching passion etc. Also, you can complete the PhD (later) while you are in the Teaching job itself. So, all in all you can do as you like. With effort.

Being an MBA degree holder with around 5 years of experience, you can try in private MBA colleges for teaching. Another option is to teach in coaching institutes for MBA. Both of these options are easy and feasible for you.
other options like big schools and colleges may ask you for B.Ed., or Ph.D. or even experience in teaching.
Once you get into teaching, you can try for better options side by side.
Another option is to pursue any short term course related to teaching like Diploma in teaching or so. This will enable you to get a job in small schools.

Ph.D. can be done along with your job. So once you become comfortable with your job, you can enroll yourself for a Ph.D. in the same institute (if available) or any other institute as per your choice.

You can also appear in Lecturership eligibility exams like CSIR-NET LS. If you secure a good rank, you can get lecturership that too in top government colleges. In this case, also, you can pursue Ph.D. side by side.

You want to make a change from the corporate job to teaching line as the corporate culture is not suiting to your temperament or in simple words it is not your cup of tea. Many people have same mental frame as you have got and in such cases teaching is definitely a better line as there is not much of on the toe activities as compared to the tough and competitive business environment.

If you are interested in teaching then there are various option from primary school teaching to post graduate levels and for them you will have to acquire relevant qualifications. For primary school teaching a diploma in teaching will be required. Some private school may give you the job just based on your present qualification but it is advisable to go for a certificate course or diploma in teaching. For teaching to high school classes generally a B.Ed. degree is mandatory and one can do B.Ed. from many regular as well as correspondence institutions in our country. If you want to get a position of lecturer in a college or university then NET exam is to be qualified and after that only one can apply for these positions. If you have interest in research then you can think of doing PhD under some good guide in a reputed institution and after that your chances of getting a lecturer job increase and you are exempted for appearing in NET. So there are many options which you have to weigh as per your calibre versus expectations from the teaching career.

Teaching career in not only limited to the above options. You have so much experience of jobs in various companies and with your MBA background you can even consider joining a coaching centre for teaching students preparing for different exams. I will like to mention that for those who have enterprising aspirations this can prove a good occupation and good career. Further, have you ever considered to join with some like minded friends or people who are running some coaching centre or opening a setup on your own? If you start on your own in a good locality covering some important subjects then believe me there is good potential in this line and once successful you can hire people like you who are desperate to move to teaching line from other stressful occupations. Please note that people generally excel in the work of their liking and choice and not in one which is being forced on them due to their qualifications. So considering all these options and aspects you have to take a conscious and diligent decision to go ahead and quench your thirst for a teaching career.

There would not be any problem in case you want to switch over the present assignment from the Corporate - sector to Teaching field. Options are not limited in the teaching profession, what is required is a cool thinking in the present scenario so as to adjust yourself with the changed profession.
MBA is one of your basic qualification and if the same is Human - resources, you could appreciate your positive traits which would make your career growth smooth.
As you have indicated Mathematics was one of your subjects during the graduation - stage. This subject if you so far remember the different portions such as Algebra, Trigonometry, Calculas, Dymamics, Vector and so on, this should be your fascinating resources in taking up assignments as a Mathematics- tutor or even the organiser of a Coaching Institure where 10+2 students are groomed further to have a seat in IIT or any prestigious colleges. In case, you want to lead as organiser apart from your involvement in Mathematics, you need two your friends interested for coaching in the subjects Physics and Chemistry respectively.
This combination would work fine in terms of earning and passion.
College Lecturership would take a lot of time in the preparation of NET and calls for your studies in the same direction.
However, make a career with your your own inclination so that interest in such an avocation is sustained.