Solution to the Problem:

(-1 + i sqrt(3)) / 2

and

(-1 - i sqrt(3)) / 2

where sqrt(3) represents the square root of 3.

To solve the problem, call the two numbers x and y.
Then y = x^2 and x = y^2.
Substituting, you get x = x^4.

So, x^4 - x = 0
Then x (x^3 - 1) = 0 so
x (x - 1) (x^2 + x + 1) = 0

Using the quadratic formula.
x = 0
x = 1
x = (-1 + i sqrt(3)) / 2
x = (-1 - i sqrt(3)) / 2

You can eliminate the first two solutions because x = y.
The other two solutions x = (-1 + i sqrt(3)) / 2 and
y = (-1 - i sqrt(3)) / 2 satisfy the given conditions.