Question 367744
First you must list all sums that will equal eleven:

10+1=11
9+2=11
8+3=11
7+4=11
6+5=11

Then you need to know which set of these numbers squared will equal 65:

10^2+1^2=100+1=101
9^2+2^2=81+4=85
8^2+3^3=64+9=73
7^2+4^2=49+16=65
6^2+5^2=36+25=61

You want the one that equals 65, so your two numbers are 6 and 5. They both add up to equal 11 and the sum of their squares is 65.