We have two numbers. Let us call them x and y. With the information that you have given, we know that the following two equations are true.

x + y = 24

x - y = 14

Now let us find a value for x by using the second equation.

x = 14 + y

Then let us substitute that value for x in the first equation.

14 + y + y = 24

2y + 14 = 24

2y = 10

y = 5

Now let us use this value for y to find the value of x.

x = 14 + y

x = 14 + 5

x = 19

Let the two numbers be 'x' and 'y'.

It is given that sum of these two numbers is 24. Therefore:

x + y = 24 ... (1)

similarly it is given that difference of these numbers equals 14. Therefore:

x - y = 14 ... (2)

We can find the values of x and y solving the above two simultaneous equation as follows>

adding equations (1) and (2) we get:

x + x + y - y = 24 - 14

2x = 10

Therefore:

x = 10/2 = 5

Substituting this value of x in equation (1) we get:

5 + y = 24

y = 24 - 5 = 19

Answer:

The two numbers are 5 and 19.

Let x and y be the numbers such that

x+y = 24 ..............(1)and

x-y = 14...............(2), assuminf x> y.

(1+2) gives: 2x = 24+14 = 38. Or x= 36/2 = 19

(1)-(2) gives: 2y = 24-14 = 10 . Or y = 10/2 = 5.