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This is quite a challenge and it is really a magic square in disguise! Here is one solution and another similar puzzle for you to try. You may like to study the articles Magic Squares and Magic Squares II.
The following puzzle comes from The Ultimate Book of Number Puzzles by Kenneth Kelsey published by The Cresset Press 1992, ISBN: 0 09 177204 4.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!