Take any 10 cards from the deck and flip them over, and make those 10 the second pile. If none of those 10 were originally face up, you have 10 face-up cards in each pile. If any of the 10 cards in the second pile was originally face-up, it will be flipped face-down, making one less face-up card in each pile, but they will still have the same number.
Good puzzle. Made me think for a while.