Question

What two numbers add up to 10 and multiply to 11

Answer 1

I don't know how you're expected to be able to solve this
in Middle School math.  Maybe I'm just out of touch and
you're doing things like this every day in Middle School.

The solution is longer than I really feel like explaining right now,
so a moderator may come along soon and delete my answer
because I didn't explain how I got it and where it came from.

The two numbers are both irrational numbers:

         5 + √14
and
         5 - √14 .

When rounded to a manageable size, they're

          8.742
and 
         1.258 .

Answer 2

Factor 11
11=1 times 11 or -1 times -11
1+11=12 not 10
-1+-11=-12 not 10
so there are no 2 numbers unless it is
what 2 numbers add up to 10 and multiply to -11 (then they would be -1 and 11)