x + y = 900 --> y = 900 - x
√x - √y = 6
√x - √(900 - x) = 6
√x = 6 + √(900 - x)
x = 36 + 12√(900 - x) + (900 - x)
12√(900 - x) = x - 36 - (900 - x)
12√(900 - x) = 2·x - 936
144(900 - x) = 4·x^2 - 3744·x + 876096
129600 - 144·x = 4·x^2 - 3744·x + 876096
4·x^2 - 3600·x + 746496 = 0 --> x = 576 ∨ x = 324
Probe
576 + 324 = 900
√576 - √324 = 6