Let's denote the unknown number as \( x \). According to the problem, the statement "One-quarter of the difference of a number and 3 is 2" can be expressed mathematically as:
\[ \frac{1}{4}(x - 3) = 2 \]
To solve this equation, first, we can multiply both sides by 4 to eliminate the fraction:
\[ x - 3 = 8 \]
Then, add 3 to both sides:
\[ x = 8 + 3 \]
\[ x = 11 \]
Thus, the number is \( \boxed{11} \).
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