Let the first number x and the second number be y.
x+y=25
x-y=7 <-- solve for x and y now
x=7+y
(7+y)+y=25 <-- substitute in the value of x found above
7+2y=25
2y=25-7
2y=18
y=18/2
y=9
x-y=7
x-9=7
x=7+9
x=16
Therefore, the two numbers are 9 and 16,
Hope I helped :)