The sum of the four numbers is $4 \cdot 15 = 60$.
Since two of the numbers are 10 and 18, the sum of the other two numbers is $60 - 10 - 18 = 32$.
Let the two equal numbers be $x$.
Then, we have the equation $x + x = 32$, which simplifies to $2x = 32$.
Solving for $x$, we find that $x = 16$.
Therefore, the product of the two equal numbers is $16 \cdot 16 = \boxed{256}$.
The answer is: 256
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
If the arithmetic mean of four numbers is 15, and two of the numbers are 10 and 18, with the other two numbers being equal, what is the product of the two equal numbers?

### Answer:
