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

From the problem, we have the following two conditions:

1. The sum of the two numbers is 18: $x + y = 18$

2. One number is 8 larger than the other: $x = y + 8$

Now, substitute the second equation into the first:

$(y + 8) + y = 18$

Simplify the equation:

$2y + 8 = 18$

Subtract 8 from both sides:

$2y = 10$

Divide both sides by 2:

$y = 5$

Now, substitute $y = 5$ into the equation $x = y + 8$:

$x = 5 + 8 = 13$

Thus, the two numbers are $13$ and $5$.

Final Answer:

The two numbers are $13$ and $5$.

Would you like a detailed breakdown or have any questions? Here are some related questions to practice:

1. If two numbers have a sum of 24 and one is 10 larger than the other, what are the numbers?
2. Solve algebraically: The sum of two numbers is 30, and one is 4 times the other.
3. The sum of two numbers is 50, and one is twice the other. Find the numbers.
4. If two numbers have a sum of 40 and one is 12 larger than the other, what are the numbers?
5. Solve: The sum of two numbers is 35, and one number is 5 more than twice the other.

Tip: When working with two variables, substitute one equation into the other to reduce the system to a single variable.