Let the two numbers be \( x \) and \( y \).
We are given the following two equations based on the problem statement:
- \( x + y = 30 \)
- \( x - y = 8 \)
To solve for \( x \) and \( y \), we can add the two equations together:
\[ (x + y) + (x - y) = 30 + 8 \]
This simplifies to:
\[ 2x = 38 \]
Now, divide both sides by 2:
\[ x = 19 \]
Next, we can substitute \( x = 19 \) back into the first equation to find \( y \):
\[ 19 + y = 30 \]
Subtracting 19 from both sides gives:
\[ y = 30 - 19 = 11 \]
Now that we have both numbers, \( x = 19 \) and \( y = 11 \), we can find their product:
\[ x \times y = 19 \times 11 \]
Calculating the product:
\[ 19 \times 11 = 209 \]
Thus, the product of the two numbers is \( \boxed{209} \).
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