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[Neonivek]

That and technically Hydrogen would count as an explosive.

Also there are quite a few substances you can put your Egg into (with a Jar I guess) that would protect it to my knowledge (Id test it first)

[Tack]

I'd say make it the base of a rubberband ball.

That should put it under enough tension that it won't break.

On Dukes idea, put the egg inside a series of exponentially larger triangular-based-pyramids. These, affix to the egg, and to the other frames with wire and sticky tape, or something stronger if you can.

[Strife26]

Note that 10 x 10 x 10 isn't much space to work with, not much more than the length of  playing card each way.

I've got no shortage of adhesives, elmers, tacking, model, krazy, super, gorillia, duct, scotch, masking, packing, double sided. I've also got a few tubes of industrial strength (the kind that need a gun). I keep a drawer full of em.

[Duke 2.0]

 Actually, the rope idea might work if you are quick with a long pole nearby with a hook on top to catch the rope.

 Also, put a red bell on the pole so you can say "You didn't say anything about long poles with a hook on the end and a red bell on it couldn't interact with the rope in flight!"

 Wait, are there rules against interacting with it in mid-flight?

[Heron TSG]

This is easy. Encase the egg in a 10x10x10 cube of D30 shock absorbing putty.

Invincibility isn't cheating!

[Tack]

If the egg fits loosely into one of the tubes, do this. Layer it with stickytape on the sides, so that it just has contact with the sides of the tube. Then, Drill holes in it on either side of the egg, and loop a multitude of rubberbands on either end.
So far, decent plan.

Then - Take a sinker, or something of that sort, and suspend it in the middle of one end of the tube.

That way, when it is dropped, or thrown, the tube will fall to the ground that end first, and therefore the egg will be suspended through it's own friction against the edges of the pipe, and the rubber bands.

[Osmosis Jones]

Does it have any restriction on changing size as it falls? Because, ya'know, I'm pretty sure you can fold a pretty large  parachute into a 10x10x5 area (leaving space for the egg).

[Tack]

On my previous Idea, I just realised a parachute would work too. Thanks, OJ.

[Duke 2.0]

 I would suggest some form of airbag approach where a bag is filled with compressed Helium while in the air and slowly decent down, but the only way to really store that Hydrogen would be a small tank, how much it could release quickly a mystery to me, or a gas generator, which would technically be an explosive that outputs cool gasses as opposed to hot ones.

 But the idea of compressed Hydrogen filling a bag seems interesting.

 Edit: Also, a modification of Tacks idea. Instead of taping the inside you fill it with various fluids of different densities. Seal the tube and attach whatever plans to the outside as you wish, including but not limited to parachutes, shock absorbers on the bottom and foam.
 As the rig hits the ground the egg will wall through fluids of increasing density, the first few layers merely slowing it down the the point where the later fluids won't break the egg under those forces.

[Reasonableman]

Or, um, maybe you could do something like this:

You can also make your device a propellor or Glider depending on where it will be dropped.

The thought popped into my head just before reading that post: you could put a propeller on it to make it fall more slowly. Helicopters use a similar principle to make an unpowered landing if I recall correctly...

Anyway, the point is, a spinning rotor atop your contraption need not be larger than your 10x10x10cm limit to create significant drag.

[Osmosis Jones]

Or cover the outside in shuttlecock fins. They're soft, AND high drag.

[Strife26]

This is easy. Encase the egg in a 10x10x10 cube of D30 shock absorbing putty.

Invincibility isn't cheating!

Where do I got about finding shock absorbing putty?

[Heron TSG]

http://www.d3olab.com/

Thar ye be.

[userpay]

Hmm thats a rather small area but one thing I would suggest is popped popcorn, acts just like packing pellets. Be glad you didn't have the restrictions my class had, we could only use string and plastic drinking straws. Suffice to say I failed that one but I got got straight A's on the next two projects. An idea though is to construct a platform for the egg device to land on.

[codezero]

You can do it without helium balloons, just force 3 regular blown up ballons in a 10^3 container with the egg in the centre.

A novel approach would be to have the egg land on it's tip, try cracking an egg between your finger and thumb lengthwise and you'll see why. The shuttlecock idea would be perfect for setting it's approach, or just put the egg in the shuttlecock with some pads.