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According to Turkey's page on Visa Information For Foreigners:
Egypt: Official passport holders are exempted from visa for their travels up to 90 days. Ordinary passport holders are required to have visa to enter Turkey. Ordinary passport holders may obtain their 30-day single-entry e-Visas via www.evisa.gov.tr, provided that they have a valid Schengen or USA, UK, Ireland visa or residence permit and that they travel to Turkey with Turkish Airlines or Egypt Air.
Besides, those ordinary passport holders who are under 20 or over 45 years old may get their 30-day single-entry e-Visas via the website www.evisa.gov.tr.
Somewhat similar requirements are shown on Timatic on Emirates.com, which also says that people eligible for e-Visas can acquire the e-Visa upon arrival at the airport. The Timatic on IATA information is slightly different, with no mention of age limits.
Given the varying information from different sites, it looks like the best plan is to use www.evisa.gov.tr ahead of time. If it works, you're all set; if not, you'll have to apply for a visa from the Turkish embassy.