We have xy = 144, x + y = 30, and x > y, we need to find x - y.

x - y = sqrt ( x - y)^2 = sqrt [ (x + y)^2 - 4xy]

=> sqrt [ 30^2 - 4* 144]

=> sqrt [ 900 - 576]

=> sqrt (324)

=> 18

**Therefore x - y = 18**

Given the equations:

x*y = 144.............(1)

x+ y= 30 .............(2)

We will use the substitution method to find the values of x and y.

from (2) we know that y= 30-x

Now we will substitute into (1).

==> x*y= 144

==> x*(30-x) = 144

Now we will open the brackets.

==> 30x - x^2 = 144

==> x^2 - 30x + 144 = 0

Now we will factor.

==> (x -24) ( x-6) = 0

==> x1= 24 ==> y1= 30-24 =6

==> x2= 6==> y2= 30-6 = 24

But we know that x>y

Then the values are : x= 24 and y= 6

Now we need to find the values of x-y

**==> x-y = 24-6 = 18**