The difference of two numbers is $4$. If the difference of their reciprocals is $\frac{4}{21}$, find the numbers.

The difference of squares of two natural numbers is $45$. The square of the smaller number is $8$ times the larger number. Find the two numbers.

Note: The question given in the textbook seems to be wrong. The correct question should be as below:

The difference of squares of two natural numbers is $45$. The square of the smaller number is $4$ times the larger number. Find the two numbers.