In the American game of "eight-ball" there are 15 numbered balls (1 through 15). At the beginning of the game, these balls are racked into a triangular pattern as shown.
The challenge this week is to place the numbers 1 through 15 into an upside-down triangle pattern such that each number is the result of *subtracting* the two numbers above it. To eliminate mirrored answers, provide a solution where the numbers at the three points of the triangle are in ascending order going clockwise.
P.S. When taking the difference, always use the absolute value. Feel free to add a comment with your answer, along with how you solved it.