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This is a very philosophical question but let's try to cut it down using physics.
Newton's 2. Law
F = m * a
If we only look at classical mechanics for this theory and keep quantum physics out, because for this to work the mass needs to be constant.
We interpret unstoppable force as a body moving really fast, thus a ( acceleration) would be very high. Call it "unstopF".
and define unmoveable object as a body that is not moving, thus acceleration would be really low or zero. Call it "unmovF"
unstopF is moving really fast and keeps going faster, so sure it must have have high kinetic energy/force.
and unmovF must have infinite mass. F = m>? * a>? -> F>? (we must keep theory of relativity out, because it would make this paradoxical question even more paradox. Because a body of infinite mass would collapse into a blackhole and the whole energy = mass * c thing... blahblah)
The third newtonian law says Fa->b = Fb->a
an object that exerts force onto another body, then the other body exerts the same amount of force into the opposite direction. So unmovF would not budge from its position and unstopF would "reflect" and keep on accelerating infinitely but in the opposite force vector it came from.
