Assign the result of explode to a variable and pass that variable to end:
$tmp = explode('.', $file_name);
$file_extension = end($tmp);
The problem is, that end requires a reference, because it modifies the internal representation of the array (i.e. it makes the current element pointer point to the last element).
The result of explode('.', $file_name) cannot be turned into a reference. This is a restriction in the PHP language, that probably exists for simplicity reasons.