Can a summoned earth elemental carry a creature with it when it is Earth Gliding?
I'm thinking of things like having your summoned elemental pull you into a wall to become unseen.
I recommend that the extraordinary ability earth glide should be treated like a variant of burrowing. Thus the limits on a creature's ability to carry—not just grapple and drag—other creatures while employing earth glide should be similar to the limits the DM's placed a creature carrying passengers while flying or (more appropriately, in my opinion) swimming.
Narratively, as most burrowers are considered to be digging using their limbs, also carrying another with those limbs should at least reduce such creatures' speeds. However, since an earth elemental just glides through the earth, this DM wouldn't impose any restrictions on him carrying a passenger. Breathing will still be the passenger's problem to solve, though.
Earth Glide: An earth elemental can glide through stone, dirt, or almost any other sort of earth except metal as easily as a fish swims through water.
I see no precident here that it would affect other creatures. I am aware of certain monsters that can move creatures thru terrain but that occurs when they are swallowed. I reviewed grappling but I don't believe there are further citations because I believe the game implies that if you cannot move somewhere you cannot move there (like you cannot fly without flight, you cannot move through walls or floors without capability to do so, etc) so doesn't specifically state it in any combat rules.