You could use a CPAN module, such as XML::Twig. The following code unconditionally replaces the text of all instances of 'count' elements with the value 14.

use strict;
use warnings;
use XML::Twig;

my $xmlStr = <<XML;
<project>
 <run_count>
  <count>13</count>
 </run_count>
</project>
XML

my $twig= new XML::Twig(
    PrettyPrint   => 'indented',
    twig_handlers => { count => \&count }
);
$twig->parse($xmlStr);
$twig->print();
exit;

sub count {
    my ($twig, $cnt) = @_;
    $cnt->set_text(14);
}  


__END__

<project>
  <run_count>
    <count>14</count>
  </run_count>
</project>
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Side note: Welcome to the Monastery. In general, it is better to use 'code' tags instead of 'pre' tags when posting code. (see Perl Monks Approved HTML tags)