How to make instant noodle with egg?
It depends on whether you're adding the water to the noodles or vice versa.

If I'm boiling the noodles on the stove for three minutes, I measure the right amount of water, and after the noodles are cooked I usually lift (most) of the noodles out of the water and into the bowl, drop the egg in and let it cook in the water while I add the seasoning to the noodles, then pour the egg (and as much water as I want) into the bowl.  I tend to lift the noodles out because they splash more when pouring, but no reason you couldn't add the egg to the noodles and water straight after they're cooked, or even during cooking.  If you do you add the egg as soon as the stove is turned off, the residual heat in the water cooks it enough.  If you don't want extra water in your noodles, you can lift it out with a slotted spoon, or pour most of the water out first, then add to your noodles.

If I'm pouring boiling water onto the noodles (already in the bowl), I add the egg first, even break the yolk and stir a little, lay the noodles on top, and pour the boiling water.  In this case, the water will cool too much to cook the egg fairly fast, so it needs to be there from the start, and almost scrambled to cook more evenly.