To do this on land, you'll have to cross Israel.. Egypt and Jordan don't share a border. There may be a ferry direct from Sharm el Sheik or Taba to Aqaba in Jordan, but I'm not confident. I'd fly back to AMM, and then home from there, keep it simple.
there is a ferry from Nuweiba to Aqaba. from Cairo, you can take a bus to Sharm el Sheikh (6 hrs), then bus or taxi to nuweiba (about 2 hrs) and then ferry. to get to Nuweiba in time for the ferry, probably have to take overnights bus from Cairo around midnight or so. not fun, but very cheap. If my memory is right, Cairo-Sharm bus was around $10. but ferry is about $50 (maybe more).