#### Answer

set of all real numbers

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|n-3|=|3-n|
,$ use the definition of absolute value equality. Then use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Since $|x|=|y|$ implies $x=y \text{ or } x=-y,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
n-3=3-n
\\\\\text{OR}\\\\
n-3=-(3-n)
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
n-3=3-n
\\\\
n+n=3+3
\\\\
2n=6
\\\\
n=\dfrac{6}{2}
\\\\
n=3
\\\\\text{OR}\\\\
n-3=-(3-n)
\\\\
n-3=-3+n
\\\\
0=0
\text{ (TRUE)}
.\end{array}
Since the solution above ended with a TRUE statement, then the solution set is the set of all real numbers.