The problem states that three times the difference of a number and 10 equals the sum of 25 and that same number. Let's denote the unknown number as \( x \).
- The difference of the number and 10 can be written as \( x - 10 \).
- Three times this difference is \( 3(x - 10) \).
- The sum of 25 and that same number is \( 25 + x \).
Putting it all together, we set up the equation:
\[ 3(x - 10) = 25 + x \]
So, the correct equation is:
\[ \boxed{3(x - 10) = 25 + x} \]