Let the two numbers be x and y such that y < x.
From the given conditions, we have:
x2 - y2 = 45 … (1)
y2 = 4x … (2)
Using (2) in (1), we have:
x2 - 4x - 45 = 0
(x - 9)(x + 5) = 0
x = 9 (Rejecting the negative value of x)
From (2), we get, y = 6 or -6
Rejecting the negative value, we have, y = 6.
Thus, the two numbers are 9 and 6.