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There is a simple way to work this out, using algabra (example used here is from attached picture).

First, you add the top 2 whole numbers already given, and subtract 2 'x', which will equal to the bottom square.

356 + 297 = 653

356 + 297 - 2x = 175

You then subtract the bottom square (in the attached example is 175) from the sum of the top 2 squares.

653 - 175 = 478

You then divide this answer by 2, giving you 'x', which in this example equals to 239.

Then, to work out the answer of 'y', you would subtract 239 from 356, which equals to 117. 117 would be 'y'.

Then, you repeat the last step to work out the number which is 'z'
175 - 117 = 15).

Final Answer:

x = 239
y = 117
z = 58