According to Newton’s Law’s of Motion, technically the egg and the wall apply the same amount of force on each other. To put simply, the deciding factor is usually mass.
Think of it like this, if two marbles were to roll towards each other at the exact same speed, but one marble was heavier then the other, the momentum will shift so that the heavier marble will continue on it’s course.
This same sort of example is applied here, except at a more extreme scale.
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