The Administration of Conscription of the Egyptian Armed Forces announced they've made travel permits available online, among other services, through their website. You'll simply enter your data and there's even the option of paying by credit cards. Then, according to the video broadcast by the Ministry of defense, the travel permit will appear online to the customs officer at the airport.
Other online services will include temporary exemption papers, and other documents. There's also a 24-hour service to answer any inquiries.