The sum of two numbers is 10.3. The difference between
the same two numbers is 2.84.
Find the two numbers.

Step-by-step explanation:

We need a system of equations for this. The first sentence in the problem tells us the first equation. "Sum" means we are adding, "is" means equals. Therefore, the first equation is

x + y = 10.3

The second sentence tells us the second equation. "Difference" means to subtract. Therefore, the second equation is

x - y = 2.84

It would be best to solve this by elimination (also called addition). Line them up one over the other so the variables also line up:

  x  +  y  =  10.3

  x  -  y  =    2.84

And as you see, when you add straight down, the y's eliminate each other, leaving us with

2x = 13.14 and divide by 2 to get that

x = 6.57

Now plug that in for x to solve for y in either one of the equations. I'll use the first one:

6.57 + y = 10.3 so

y = 3.73