Prove:

Let the number of 1 ~ 9 be divided into two groups-group A and group B. (A and B can only be integers, depending on the subject conditions)

Yes: A+B=45. - ( 1)

If yes: A-B = 10-(2)

Then (1)+(2) has: 2A=55, which means A=25.5. It is not an integer, which obviously does not meet the conditions of the topic.

Therefore, there is no solution to this problem.