To solve for the two numbers, let’s denote them as x and y.
We know from the problem statement:
- The sum of the two numbers: x + y = 18
- Their difference: x – y = 2
We can solve this system of equations step by step.
1. First, we can express one variable in terms of the other from the second equation. From x – y = 2, we can isolate x:
x = y + 2
2. Now we can substitute this expression for x into the first equation:
(y + 2) + y = 18
3. Combining like terms gives us:
2y + 2 = 18
4. Next, we subtract 2 from both sides:
2y = 16
5. Now, dividing both sides by 2 yields:
y = 8
6. Now that we have y, we can find x using the expression we derived earlier:
x = 8 + 2 = 10
Finally, the two numbers are x = 10 and y = 8.
In conclusion, the two numbers you’re looking for are 10 and 8.