The difference between the squares of two consecutive numbers is 35. The numbers are?

Sure, let's solve this step by step.

Step 1: Let's denote the two consecutive numbers as n and n+1.

Step 2: According to the problem, the difference between the squares of these two numbers is 35. So, we can write the equation as:

(n+1)^2 - n^2 = 35

Step 3: Simplify the equation. The left side of the equation can be expanded to n^2 + 2n + 1 - n^2.

Step 4: Further simplifying, we get 2n + 1 = 35.

Step 5: Solving for n, we subtract 1 from both sides to get 2n = 34.

Step 6: Finally, divide both sides by 2 to solve for n. We get n = 17.

So, the two consecutive numbers are 17 and 18.