No. It is illegal to work on an eVisa.
However, if your trip to Egypt is work-related, you may be eligible for a work permit that must be applied for by your employer.
A work permit for Egypt can be granted by the Ministry of Manpower & Immigration in Egypt but must be applied for by the expat’s employer. This work permit is lasts 1 year, but is extendable for up to 5 years.