Let us assume the two unknown numbers to be "x" and "y".
Then
x + y = 37
And
xy = - 210
x = - 210/y
Now let us put the value of "x" in the first equation, we get
x + y = 37
- (210/y) + y = 37
y^2 - 210 = 37y
y^2 - 37y - 210 = 0
y^2 - 42y + 5y - 210 = 0
y(y - 42) + 5(y - 42) = 0
(y - 42)(y + 5) = 0
So when
y - 42 = 0
y = 42
Then
x = -(210/42)
= - 5
Again when
y + 5 = 0
y = -5
Then
x = 42
So the two unknown numbers are 42 and -5. I hope the procedure is clear enough for you to understand.