The sum of two numbers is 56. their difference is 18.

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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