Step 1: Firstly, write down the values and terms given in the question

The sum of two numbers = 82

The difference of two numbers= 34

Step 2: Secondly, try to realize which values that i need to find.

Step 3: In the next, Select a variable to represent one unknown value

 assume, one number = x

 Step 4: now, represent other unknown value in terms of  other chosen variable.

  assume, the other number= y

Step 5: After that, write down in words the terms and conditions given in the question in terms of variable, 

as per problems, x+y = 82 and x-y = 34

Step 6: In the last, write the word problems as equation

     x+y = 82.........  equation (1)

    x-y = 34............ equation (2)

Step 7: Finally, solve the two equation.

   at first, we will add the two equation to determine one unknown value.  After that, we will subtract the two equation to calculate the other unknown value.

by adding (1) & (2)

   x+y = 82.........  equation (1)

    x-y = 34............ equation (2)

 2x = 116

  x = 58

by subtracting the two equation we get,

2y = 48

y = 24

One number is 58 & the other is 24 (Ans)

Step 8: Check the answer.