correct answer is: a) 672 & 368

Explanation

Let, one number is ‘x’
Another number is ‘y’
According to the question,
\left(x+y\right)=1040
\rightarrow x=1040-y ----(1)
And, \left(x-y\right)=304
\rightarrow x=304+y ----(2)
So, from (1) & (2) we get,
1040-y=304+y
\rightarrow-y-y=304-1040
\rightarrow-2y=-736
\rightarrow y=\large\frac{-736}{-2}
\therefore y=368
Put the value in no (1) equation, we get:
x=1040-368
\rightarrow x=672
\therefore One number is 672 and another number is 368 .
Ans: The numbers are 672 & 368.

An additional variation of this particular query can be considered:
1. Find the two numbers when their sum is 1040 and the difference between them is 304.
2. Calculate the numbers given their sum is 1040 and the difference between them is 304.
3. What are the two numbers if their sum is 1040 and their difference is 304?