Iam thinking of two numbers. the difference of the two numbers is 36. their sum is 286. what are the two numbers i am thinking of?

Let's call the two numbers a and b. So we know that the difference of the two numbers is 36:

a - b = 36

And we know that their sum is 286:

a + b = 286

We can use either of these equations to solve for one of the variables in terms of the other variable. Let's use the first and solve for a:

a - b = 36

a = 36 + b

Now we plug this into the other equation and solve for b there:

(36 + b) + b = 286 

36 + 2b = 286

2b = 250

b = 125

Let those 2 numbers be x and y, with x>y (needed for the subtraction to put the bigger number first to get a positive answer).
"The difference of the two numbers is 36"  can be represented by the equation x - y = 36
"Their sum is 286" can be represented by the equation x + y=286.

We can now create  a system:
x - y = 36 (1)
x + y = 286 (2)

In the equation (1), let's find the value of x:
x - y = 36
Add y in both sides so we can get x on a side and its value on the other:
x - y + y = 36 + y
x = 36 + y

In the equation (2), let's replace x by its found value to find the value of y:
x + y = 286
36 + y + y = 286
2y + 36 = 286
Subtract 36 from each side so we can get the variable on a side and the numbers on another:
2y + 36 = 286
2y + 36 - 36 = 286 - 36
2y = 250
Divide both sides by 2 so we can get the variable y on a side, and its value on the other:
(2y)/2 = 250/2
y = 125.

In equation (1), let's replace y by it's value to find the numeric value of x:
x - y = 36
x - 125 = 36
Let's 125 in each side to get x on a side and its value on the other:
x - 125 + 125 = 36 + 125
x = 161

You can re-check your answer (Very important):
x - y = 161 - 125 = 36 (The difference of the 2 numbers is 36)
x + y = 161 + 125 = 286 (their sum is 286)
The answer has been approved.

Hope this Helps! :)