Let’s solve this step by step:

Problem:

We have two conditions:

1. The difference of twice a number and another number is 5.
2. The sum of the two numbers is 19.

Let the two numbers be $x$ and $y$, where $x < y$.

Step 1: Translate into equations

From the problem:

1. $2x - y = 5$ (Difference of twice $x$ and $y$ is 5)
2. $x + y = 19$ (Sum of $x$ and $y$ is 19)

Step 2: Solve the system of equations

From the second equation: $y = 19 - x$

Substitute $y = 19 - x$ into the first equation: $2x - (19 - x) = 5$ Simplify: $2x - 19 + x = 5$ $3x - 19 = 5$ $3x = 24$ $x = 8$

Substitute $x = 8$ into $y = 19 - x$: $y = 19 - 8 = 11$

Step 3: Write the numbers in order

The two numbers are: $\boxed{8 \text{ and } 11}$

Let me know if you'd like more details or have any questions! Here are some related problems for further practice:

1. Solve for two numbers where the sum is 25 and the difference is 7.
2. Solve for two numbers where the sum is 50 and twice the smaller number equals the larger number.
3. Solve a system of equations where $3x + 2y = 18$ and $x - y = 2$.
4. What happens if the difference of twice a number and another number equals 0?
5. Can you create your own problem based on this structure? Try solving it!

Tip: Always substitute one equation into the other to reduce variables when solving systems of equations!