I was always interested in electronics so I earned an Electrical Engineering degree and started my working career designing circuits for microprocessor-based Strip Chart Recording products (another engineer was responsible for creating the software). It didn't take me long to realize that the biggest contributions to the product were being made in the software. The hardware was more difficult and costly to change and upgrade (in the field). But the software could much more easily be upgraded and most of the product functions were determined by the software. With that knowledge, I switched to a software consulting job where I wrote software for many different products and industries (electronic weighing systems, payphones, steel manufacturing, software safety systems for nuclear reactors, and aluminum foundry measurement). I then moved to freight locomotive braking systems and mass transit control systems. In all of these applications, I used my knowledge of the hardware to write software that controlled products, typically called "embedded applications" (like cars, cellphones, game consoles, robotics, health industry products, automated equipment, airline and space applications, etc). These differ from IT or commercial software which typically runs on a standalone computer and does not actually control things (they instead generate reports and analyze/process/monitor data).
The range of products and applications using software is huge and growing constantly so you can focus your career on the areas that you find to be the most interesting.
FYI... I found that I could learn and work with software from home much more easily and for less money than I could with hardware so I was always (and still do) working on interesting projects.
Note: Your question used the term "Software Engineer" which indicates you are leaning towards the scientific applications/degree (CE or SE) and not to the commercial/degree (IT).
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So benefits I've gained are, I work remote now and can easily move around with my wife when the military demands it, salary is higher, flexible PTO and I am learning constantly. All things I was looking for in my change of careers. I do miss teaching and one day I hope to merge the two careers.
I was good at Math and good analytical skills and it wad a natural progression to go on this field. This was more than 40 years ago.
One of the biggest joy for me was the software that I worked on was used by the most telecom equipment manufacturers which was used by the service providers all around the globe. This was one of the satisfying moment for me beyond making money (I was paid well).
Developing software and having it used by the millions - I can say that I was part of the transformation from the wireline to wireless industry.
Whatever you do in the software - the end goal is to make a difference in the world