[IanCal]

You don’t have to do all that.

If you have a+b and a-b you’ll get 2a when added together.

So knowing just the sum we can say that a is 9 in this setup.

Now we need to figure out b.

Multiplying out those you get

a^2 + ab -ab - b^2

And I get a longing for not having started this a phone.

Cancels and fill in what we know and we get 81 - b^2 = 37

b = sqrt(44) = sqrt(4)*sqrt(11) = 2sqrt(11)

[lupire]

None of this is required for solving the problem in your head. All that is required is the ability to add 1-digit unit fractions in your head, as the problem requests.