Cool little script. I've used Algorithm::Combinatorics as well recently and found it to be a very helpful module.

Here's your script streamlined just a little bit. As the documentation points out, variations(\@data, scalar @data) is equivalent to permutations(\@data).

use Algorithm::Combinatorics qw(permutations);

use strict;

my @numbers = qw(9 -4 8 6 10);
my @operators = qw(+ - * /);
my $total = 7; #required result

my $num_iter = permutations(\@numbers);
while (my $nums = $num_iter->next){
    my $op_iter = permutations(\@operators);
    while (my $ops = $op_iter->next) {
        my $str = $nums->[0];
        $str = "($str $ops->[$_] " . $nums->[$_+1] . ")" for (0..3);

        if ($total == eval $str) {
            print "$str = $total\n";
        }
    }
}
[download]