Final answer:
The question involves simple algebra to find two numbers with a given sum and difference. The solution involves adding equations to eliminate one variable and solving for the other. The two numbers are found to be 186 and 152.
Step-by-step explanation:
The question pertains to finding two numbers given that the difference of the numbers is 34 and their sum is 338.
Let's denote the two unknown numbers as x and y. According to the problem, x - y = 34 and x + y = 338. To solve these equations simultaneously, you can add them together to eliminate y.
Adding x - y = 34 and x + y = 338 gives 2x = 372. Dividing both sides by 2 gives x = 186. Now, using the second equation x + y = 338 and substituting x with 186 gives 186 + y = 338. Subtracting 186 from both sides of the equation gives y = 152.
Therefore, the two numbers are 186 and 152.