Let's call the two numbers x and y. We're given two pieces of information:

The difference between the two numbers is 11: x - y = 11.

One-fifth of their sum is 9: (1/5)(x + y) = 9.

We can start by solving the first equation for one of the variables and then substitute it into the second equation:

From the first equation, we can express y in terms of x: y = x - 11.

Now, substitute this expression for y into the second equation:

(1/5)(x + x - 11) = 9

Now, simplify and solve for x:

(1/5)(2x - 11) = 9

Multiply both sides by 5 to get rid of the fraction:

2x - 11 = 45

Add 11 to both sides:

2x = 45 + 11 2x = 56

Now, divide by 2:

x = 56 / 2 x = 28

Now that we have found x, we can find y using the first equation:

y = x - 11 y = 28 - 11 y = 17

So, the two numbers are 28 and 17.