Write the equation that satisfies the parameters: 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 \( x \). According to the given parameters, we need to set up the equation as follows:

Start by expressing the difference of the number and 10:

- The difference of a number \( x \) and 10 can be written as \( x - 10 \).

Now, according to the problem, three times this difference is equal to the sum of 25 and the same number:

- Three times the difference is: \( 3(x - 10) \).
- The sum of 25 and the same number is: \( 25 + x \).

Putting it all together, we can write the equation:

\[
3(x - 10) = 25 + x
\]

This is the equation that satisfies the parameters given in the problem.