When to go to Jordan
Jordan has a typically Middle Eastern climate in which summers are very hot, with temperatures reaching up into the forties celsius. If you are not adversely affected by heat it is still worth considering a trip at this time as you will have sights like Petra almost to yourself.
Spring and autumn are the best times to travel as the days are warm, with temperatures into the high twenties celsius with cool nights.
Winters can be surprisingly harsh: Petra has sometimes experienced snow, and the nights get cold especially in the desert regions. Winter is also when the majority of the rain falls, but showers tend to be short and sharp.
When to go to Egypt
Traditionally Egypt has been seen as a winter destination, with most visitors arriving between October and April. At this time of year, Cairo and Lower Egypt (the area towards the Mediterranean) are pleasantly cool, with average maximum temperatures in the low twenties celsius.
Upper Egypt (around Aswan and Luxor) tends to be a few degrees warmer, but still very pleasant. There may be some rain in Lower Egypt, but it is light and sporadic.
The summer season from May to September is hot, especially in Upper Egypt where temperatures can hit 50C. The high temperatures are, however, alleviated by very dry air, airconditioning, far fewer visitors and lower prices, making summer a viable season for your trip.