One number is 7 more than another. the difference between their squares is 161. what are the numbers?

X is 7 more than y
x>y then
difference betwen squares is 161 so

x=7+y
and
x²-y²=161

so
x=7+y
sub that for x in other equation

(7+y)²-y²=161
y²+14y+49-y²=161
14y+49=161
minus 49 both sides
14y=112
divide both sides by 14
y=8

sub back

x=7+y
x=7+8
x=15

the numbers are 15 and 8

Let n be your first number and n+7 be the second. Then:
n²+161=(n+7)²
n²+161=n²+14n+49
14n=112
n=8
n+7=15
Your two numbers are 8 and 15. ☺☺☺☺