I'm not familiar with the habits of the Egyptian tortoises, however, in other testudo species it's not uncommon for them to bury themselves. They do this to feel safe while they're resting, or to escape the heat, or to reach moisture.
That's what they do. If you notice they have the ability to splay there had limbs sideways too. They also have a semi hinge on their plastron. This is so when they do burrow under trees, bushes and shelter they can open the hinge and pull the bundles sideways and tuck in to escape from extreme heat. All of mine do this burrow like behavior during the day. Offer numerous hides for both of them. The female will find the one she likes.