The larger number is 5.
<u><em>Explanation</em></u>
Lets assume, the larger number is
and the smaller number is 
As the sum of two numbers is 9, so...

Now, the sum of their squares is 41, so....

First, solving equation (1) for
....

Now, plugging this
into equation (2) , we will get...

If
then 
So, the larger number is 5.