Let's denote the unknown number as \( x \). According to the problem, one-quarter of the difference of the number and 3 is equal to 2. This can be expressed in the following equation:
\[ \frac{1}{4}(x - 3) = 2 \]
To solve for \( x \), first multiply both sides of the equation by 4:
\[ x - 3 = 8 \]
Next, add 3 to both sides of the equation:
\[ x = 8 + 3 \]
\[ x = 11 \]
Thus, the number is \( \boxed{11} \).