It is hard to find work in Egypt as a local, let alone as a foreigner. My husband is Egyptian, and he knows that the only way, really, for him to get a job if he wanted one would be to go there and network until something comes up, which for him it would as he has a reputation in the community. But for you I think you need to approach the International Schools for jobs for your husband in teaching. They advertise widely overseas and interview abroad for jobs. If you go that route you can expect a higher salary and visas to be dealt with for you. As long as one of you has a job the other can sort themselves out when they get there. There are lots of International Schools in New Cairo and you can find them all online.
Hope this helps.