This Limited Edition item was available for 450 MC from October 7-22, 2010 and gave 1 xp when bought. The description reads "Contains 1 of 5 exclusive MC surprises, each with an exotic Egyptian theme!" True to its description, all items inside the Egyptian Mystery Crate cannot be bought elsewhere. What you get from the Egyptian Mystery Crate is entirely random however, so there is no way to pick and choose, or to "increase" your chances. It is possible to receive the same item more than once if you purchase the crate more than once.
This crate is not the same object as the Mystery Crate or the Mystery Gift Box, nor will it give the same items as the other two.