The sum of two numbers is 37, and the difference of their squares is 185. What is the difference between the two numbers?

Let the two numbers be $a$ and $b$.

Given:
$a + b = 37$
$a^2 - b^2 = 185$

Step 1: Use identity

$a^2 - b^2 = (a - b)(a + b)$

So,
$(a - b)(a + b) = 185$

Step 2: Substitute

$(a - b) \times 37 = 185$

Step 3: Solve

$a - b = \frac{185}{37} = 5$

Final Answer: 5