The diffrence between two positive numbers is 7 and the square of thier sum is 289​

You can use substitution method
x - y = 7
(x+y)^2=289
So
Since the square of their sum is 298, their sum without being squared is the square root of 289.
Hence,
x - y = 7
x + y = 17
By subtracting you get the following:
= (0) -2(y)=-10
So -2y=-10
y=-10/-2
y=5
Now, plug in y in both equations to get x
x - (5) = 7
x + (5) = 17
Multiply each equation with its opposite y variables
(5) x - (5) = 7
(-5) x + (5) = 17
= 5x -25 = 35
-5x -25 = -85
Now subtract the equations
= 10x + (0) = 120
10x = 120
x = 120/10
x = 12