The problem states:

• The sum of two numbers is 90.
• Their difference is 12.
• We are asked to find the two numbers.

Let the two numbers be represented by $x$ and $y$.

We have the following system of equations:

1. $x + y = 90$ (the sum of the two numbers)
2. $x - y = 12$ (the difference of the two numbers)

Now, we can solve this system of equations using the addition method. By adding both equations:

$(x + y) + (x - y) = 90 + 12$

Simplifying:

$2x = 102$

Solving for $x$:

$x = \frac{102}{2} = 51$

Now substitute $x = 51$ into the first equation $x + y = 90$:

$51 + y = 90$

Solving for $y$:

$y = 90 - 51 = 39$

Thus, the two numbers are $51$ and $39$.

Would you like further details on how I solved this? Or do you have another question?

Here are some related questions you can explore:

1. How do you solve systems of linear equations by substitution?
2. What are some real-world applications of systems of equations?
3. How do you graph the solutions to a system of linear equations?
4. How can we solve a system of equations if one equation involves multiplication?
5. How do you check the solution to a system of equations?

Tip: When solving systems of equations, always check your solutions by substituting them back into the original equations to verify they satisfy both equations.