How difficult is it to get an academic position in applied mathematics when your PhD is in electrical engineering?
How difficult it is to get a position in another field depends enormously on your specific interests and background.  Moving from electrical engineering to applied mathematics may be pretty reasonable, since there are some research areas that are widely considered part of both fields, such as control theory.  If you already work in the intersection, then you'll have some flexibility in your job search.  You'll have a much tougher time if you're proposing to change your research interests, or if you work on a topic that is not commonly studied in applied math departments, even if it could be.

A first test is whether you can find anyone with your background and interests in an applied math department.  If you can't find anyone, then it may be difficult to become the first.  (It could still be worth a try, but you shouldn't get your heart set on doing something unprecedented.)  If you can find such people, then you have role models.  At that point, you can start looking at the web pages and CVs of people who have made the transition.  Where do they publish?  How do they present themselves and their work?  Can you see any differences from people working in electrical engineering?  Of course you don't need to imitate these people too closely, but at least you'll have examples of what has been well received by applied math departments.  Some things can be adjusted on short notice, while others take time.  If you're a little further from fitting in, doing a postdoc in applied math may help bridge the gap.