The numbers are 37 and 19
From the question,
Let the numbers be x and y
From the first statement
The sum of two numbers is 56.
That is,
x + y = 56 --------- (1)
From the second statement
Their difference is 18
That is,
x - y = 18 ----------- (2)
Add equations (1) and (2)
x + y + x - y = 56 + 18
2x = 74
∴ x = 74 ÷ 2
x = 37
Substitute the value of x into equation (1) to determine the value of y
x + y = 56
37 + y = 56
y = 56 - 37
y = 19
∴ x = 37 and y = 19
Hence, the numbers are 37 and 19.
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