there's no way to open an egyptian account and access it in the US. you can open an international account with an international bank in the US - they have special expat accounts - but I think you need to place btw 5-10,000 USD to open such an account.alternatively, you can simply open a foreign currency account - savings - in a bank like EAB in Egypt and wire the money to your account in the states. it takes about 24 hrs for the transfer and costs around $30. If you're talking about personal use (thousands of dollars) as opposed to bsn use (tens of thousands) this is your easiest option.
you'll need an address and a passport to open an account in Egypt (but you don't need to show proof of residency/your rent lease)