I have an EE degree and was in embedded for a few years. I kept getting hired for that one problem, then was no longer needed. All the jobs I could find were short term contract work or "Thanks for fixing that, now we don't need you" situations. I still get emails about short term, in office work in the Midwest. I enjoyed the work but I couldn't find stable employment. Embedded worked out to be a good transition to software and then web development though.