A difference pyramid

Here is a “simple” problem my 7-year-old son was given for homework.

The task is to put the numbers 1 to 10 into the pyramid so that each number appears once and is the difference of the two numbers in the blocks below it.

I have started to fill in the pyramid. You can see that 1 is the difference of 3 and 4. This is for explanation only and you should start from an empty pyramid.{format changed to bold after publication -jb}

If you cannot find a solution, can you prove that there is no solution? Can you derive any constraints?

This is tough one. I solved it after about 2 hours. Good luck