Flipped the circuit breaker off, unscrewed the old one and disconnected the wire. I clipped a clothes pin to the wire so it would not get pulled into the back wall. On the other side the wire stayed in the back wall when I pulled the element out. I had to pull out the oven and climb behind it to fish the wire through. It turns out that when the oven was originally put together the wire was caught under a nearby cover plate on the oven back. Once freed, I was able to stick the wire back through the insulation. After that it was easy to connect the wires and screw the element in place.
If not for the stuck wire, I would have finished in 5 minutes by myself. I needed a helper to catch the wire as it was fished from the back. All considered, it was a very easy fix.