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Let's solve this problem step-by-step.

STEP-BY-STEP SOLUTION:

We will be using simultaneous equations to solve this problem.

Let's first establish the equations which we will require to solve this problem as displayed below:

Let number no. 1 = x

Let number no. 2 = y

Equation No. 1 -

x + y = 59

Equation No. 2 -

x - y = 11

To begin with, we will make ( x ) the subject in the first equation as displayed below:

Equation No. 1 -

x + y = 59

x = 59 - y

Next we will substitute the value of ( x ) from the first equation into the second equation to solve for ( y ) as displayed below:

Equation No. 2 -

x - y = 11

( 59 - y ) - y = 11

- y - y = 11 - 59

- 2y = - 48

y = - 48 / - 2

y = 48 / 2

y = 24

Then we will substitute the value of ( y ) from the second equation into the first equation to solve for ( x ) as displayed below:

Equation No. 1 -

x = 59 - y

x = 59 - ( 24 )

x = 35

FINAL ANSWER:

Therefore, the two numbers are 35 and 24.

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