Taipei is 5 hours ahead of Cairo
Best overlap: 8:00 AM to 1:00 PM in Cairo is 1:00 PM to 6:00 PM in Taipei.
The hours that work for both Cairo and Taipei are 8:00 AM to 1:00 PM (Cairo) and 1:00 PM to 6:00 PM (Taipei). The shared window is roughly 5 hours; treat its midpoint as the default and you'll keep both teams happy. Note the seasonal wrinkle: when Cairo is on daylight saving and Taipei isn't, the gap between them grows or shrinks by an hour.