use strict;
use Tie::File;

# read first file
open my $fh, '<', 'FILE1'
	or die "can't open FILE1\n";
chomp(my @file1 = <$fh>);
close $fh;

# remove from second file
tie my @file2, 'Tie::File', 'FILE2' 
	or die "can't open FILE2\n";

foreach my $x (@file1) {
	@file2 = grep {!/^$x$/} @file2;
}

untie @file2;