The following should work; I haven't had the guts to run it on your real data yet, but my mini-testset seems to result in an answer...

#!/usr/bin/perl

=cut
my @t = (
          '18.930167',
          '17.967469',
          '0.008720',
          '0.008720',
          '122.640000',
          '12493.320000',
          '359.520000',
          '288.700000',
          '359.520000',
          '89.880000',
          '32.960000',
          '56.920000',
          '13.470000',
          '1231.360000',
          '20587.440000',
          '359.520000',
          '792.170000',
          '629.160000',
          '972.290000',
);

my $target = 843.24;
=cut

my @t = (100,2,32,4,65);
my $target = 7;

my @terms = _test($target,@t);
for my $n (0..$#terms) {
    next unless $terms[$n];
    print (($terms[$n]<0)?'subtract':'add');
    print " value number ",$n+1," (",$t[$n],")";
    print "\n";
}
print "to obtain total of $target\n";
sub _test {
        my ($target,$number,@rest) = @_;
        for my $term (0,$number,-$number) {
                if(@rest==0) {
                        next unless $target == sprintf('%.2f',$sum+$te
+rm);
                        return ($term/$number)
                }
                my @terms = _test(sprintf('%.2f',$target-$term),@rest)
+;
                next unless @terms;
                return (($term/$number),@terms);
        }
        return;
}
[download]

It's a recursive algorithm that will eventually try every possibility until it finds a working set of terms... It will probably take a long time with the real dataset, so you'll want to eliminate as many terms as possible beforehand.