#### Answer

$x + y = 62$
$y = x + 12$
One number is $25$; the other number is $37$.

#### Work Step by Step

If the sum of two numbers is $62$, then let us set the first number as $x$ and the second number as $y$. If we add them together, we should get $62$. Let us write an equation reflecting these details:
$$x + y = 62$$
Let us set the second equation as $y$ being the larger number. We know that the larger number is $12$ more than the other number, so we have:
$$y = x + 12$$
We can use the substitution method to substitute this expression in for $y$ in the first equation:
$$x + (x + 12) = 62$$
Group like terms:
$$(x + x) + 12 = 62$$
Combine like terms:
$$2x + 12 = 62$$
Isolate the $x$ term by subtracting $12$ from both sides of the equation:
$$2x = 50$$
Divide both sides by $2$ to solve for $x$:
$$x = 25$$
Now that we have a value for $x$, we can plug this value into the second equation to come up with the value for $y$:
$$y = 25 + 12$$
$$y = 37$$
One number is $25$; the other number is $37$.