Welcome to FT, Rob French.

No one, other than Egypt Air, can answer your question. Have you tried calling them?

All airlines treat this upgrading process differently. Some don't allow any upgrading (using cash or miles) from economy to business (i.e. you don't get credit for your economy ticket, but of course you can buy a business class ticket), while others allow it only from certain higher-fare economy ticket. Some make random availability, while others allow you to pay for an upgrade as a matter of course. I think that the closest answer I can give you is that, if it is possible, the cost will be about the same as the difference in price between economy and business in the first place.