If file 2 is fairly small, I'd put that file into a hash:

my %file_data;
open( my $fh, '<', "/path/to/file2" ) or die $!;
while(<>) {
    chomp;
    $file_data{$_} = $.;
}
close $fh;
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You can then go through file1 line-by-line and lookup the hash entry. The value will be the line number that entry is on.