G'day emdub,

Welcome to the monastery.

The following code shows how you could handle multiple pairs of strings. I've hard-coded a space to match your "Output". You haven't indicated exactly what you mean by "letter": I've used any character matching /\p{Alpha}/ (see "perluniprops: Properties accessible through \p{} and \P{}") — your concept of "letter" may differ.

#!/usr/bin/env perl -l

use strict;
use warnings;

my @pairs = (['CHARLIE ROOT', 'HARRY NODE'], ['abc1', 'cde1']);

print get_non_shared(reverse @$_), ' ', get_non_shared(@$_) for @pairs
+;

sub get_non_shared {
    my ($ref, $src) = @_;
    my %ref_char = map { $_ => 1 } grep { /\p{Alpha}/ } split '' => $r
+ef;
    join '' => grep { ! $ref_char{$_} } split '' => $src;
}
[download]

Output:

CLI T Y ND
ab1 de1
[download]

Note that you haven't indicated how you get your pairs of strings nor what combinations are involved in the operations. Does one string equate to one line from a file? Are you operating on just single pairs from matching lines (i.e. ~300 operations) or all possible combinations (i.e. ~90,000 operations)? Depending on the answers to those — and potentially other questions, such as how often do you plan to run the program — some efficiency optimisations may be useful.