That's an interesting question. I know a guy who was (is) an ME. He worked in the auto industry calibrating ABS and traction control systems. That's an area where torques/forces/dynamics are required, but no real software background. He would either come up with new ideas, or try to track down bugs in the algorithms - he had access to the code since we were all at the same company. He moved on to fixing problems (the software team had a lot of things to do so weren't as responsive as he wanted?) and even implementing features. When I met him he was a solid embedded software engineer and I was a bit surprised to hear his path to get there.
So I guess find some niche that has overlap between what you know and what you want to do. Then gradually leverage that as you improve (and prove to others) your capability in the "other" area. How you find that overlap is up to you. For one guy it meant calibrating stability control systems was the start.
I've come to think the most flexible place to branch out from is product testing or manufacturing. You can learn a lot about a lot of different aspects of things there. Just don't let yourself stagnate.