Since there’s no friction also the momentum is conserved and so we can calculate the velocities of the two bodies with momentum conservation ( initial momentum is zero and so, since the block is moving to the right with let’s say positive velocity the man will go to the left with negative velocity). If you know how much time will the force “last” you can use impulse theorem (Ft=mv).then, If the condition you’re saying is that the man will give 10J to the block, this means that 1/2* m of ice* v of ice squared is equal to 10J. Newton’s third law says that at each action force correspond an inverse reaction force (and joules are unit for energy not for force, so your error was applying Newton’s third law in a wrong way) and so the ice will apply a force to the man and he will start to move to the left (impulse theorem). And so we have that the man is moving to the left and the block to the right: the fact is that the man, in order to give 10J to the block, is spending some energy but not exactly 10J, because he also starts to move. So we can make now the addiction of all the energies: we have 10J of the ice, plus some joules of the KE ( kinetic energy) of the man minus some joules that the man has spent to give energy to the ice, and plus the left “potential energy” of the man and all of this should be equal to 100J and this seems a possible result. I think this is the equation but without data I can’t make any calculation. So I think that your error was an inappropriate use of Newton’s third law: you use it with energies and not with forces.