The difference between two positive integers is 3.If the sum of their squares is 369,what is the sum of the numbers.?

Let the first positive integer = x
then the second positive integer = x - 3
Now, according to question, we have 
$$\begin{gathered} x^2 + {\left(x - 3\right)}^2 = 369 \\ \Rightarrow x^2 + x^2 + 9 - 6x = 369 \\ \Rightarrow 2x^2 - 6x - 360 = 0 \\ \Rightarrow 2\left(x^2 - 3x - 180\right) = 0 \\ \Rightarrow x^2 - 3x - 180 = 0 \\ \Rightarrow x^2 - 15x + 12x - 180 = 0 \\ \Rightarrow x \left(x - 15\right) + 12 \left(x - 15\right) = 0 \\ \Rightarrow \left(x - 15\right) \left(x + 12\right) = 0 \\ \Rightarrow x - 15 = 0 or x + 12 = 0 \\ \Rightarrow x = 15 or x = -12 \left(rejected\right) \end{gathered}$$

Hence the first positive integer = x = 15
second positive integer = x - 3 = 15 - 3 = 12