Note that top left and bottom right squares have to be the same number. Let those boxes be x.
Now, let top right be y, such that x + y = 8
Hence, let the remaining box be z, such that x + z = 13 and z - x = 6
Let's rewrite that so that we have three equations.
x + y = 8
x + z = 13
z - x = 6
Since x appears in all of them, intuitively we should eliminate x.
From (2), x = 13 - z
Then our new equations are:
13 - z + y = 8
z - (13 - z) = 6, since (2) is useless to us now.
From (3), 2z - 13 = 6
2z = 19 and z = 19/2
We have z (bottom right).
We can substitute z to find x.
x = 13 - 19/2 = 7/2
Hence, y = 8 - y = 9/2
Therefore, going left to right, up-down:
7/2 + 9/2 = 8 (true)
19/2 - 7/2 = 6 (true)
7/2 + 19/2 = 13 (true)
9/2 + 7/2 = 8 (true)
