The difference between my digits is 7. When you divide me by the sum of my digits, the quotient is the sum of my digits. That makes me a perfect you know what! Which number am I?

To find the number, let's break down the given information.

1. The difference between the digits is 7: Let's assume the two digits of the number are x and y, where x is the larger digit. So, x - y = 7.

2. When you divide the number by the sum of its digits, the quotient is the sum of its digits: This means that the number, let's call it xy, should satisfy the equation xy / (x + y) = x + y.

Now, let's solve these equations step by step:

From the first equation, x - y = 7, we can rewrite it as x = 7 + y.

Substituting this value of x in the second equation, we get:

(7 + y)y / (7 + y + y) = 7 + y

Simplifying further:

(7 + y)y / (7 + 2y) = 7 + y

Cross-multiplying:

(7 + y)y = (7 + y)(7 + 2y)

Expanding:

7y + y^2 = 49 + 7y + 14y + 2y^2

Rearranging and simplifying:

y^2 - 21y + 49 = 0

Now, we can solve this quadratic equation.

Factoring is convenient for this equation:

(y - 7)(y - 7) = 0

So, y = 7.

Substituting this value of y into x = 7 + y, we get x = 7 + 7 = 14.

Therefore, the number that satisfies the given conditions is 14.