In theory yes but to start with we need to know where you are starting from, I will assume somewhere in Europe. At the moment there are well reported problems in Syria which effectively block coming in from the east, others may know a way around this but I cannot see one. The other way is from the west which means going through Libya which I believe is possible, details have already been posted on this site if you search, you need to get the ferry from France to Tunisia to start with.
You also need to bear in mind the cost of a carnet for Egypt, which is the highest in the world, details also on this site in trip paperwork.
If gaffer tape doesn't fix it then you haven't used enough tape