Okay, just assume there's gravity strong enough that no matter how much work we put into vertical work, it will not move.
Work in this case, is split into two components, vertical and horizontal. Since we are ignoring the vertical component (because we'll assume something like the normal force by the ground + Force applied by you upwards = gravitational force).
So we only have to find the horizontal component.
But we don't even know the force applied yet.
We can't solve the amount of energy given to the crate without an external force, so information wise, yes it seems unsolvable unless you were given extra information.