This is a hard question. I managed to make the switch myself a few months ago by dumb luck. A co-worker of mine designed a piece of hardware that caught some attention in local tech scene, and a consumer electronics company that was looking for consultants interviewed him and some of his co-workers. I passed, and now I'm some kind of embedded developer.

I have been in a job that was supposed to include both. It was a complete bait and switch deal, in the end most that I did was writing non-web integration code and tests. Though I didn't get much experience from actually implementing their algorithms, I knew enough of them and linear algebra to be recruited at a graphics middleware company... unfortunately that didn't last.

The CV doesn't really matter. After the graphics company had let me go, I had zero Web experience and was still hired for a backend CRUD job.