You could use your TicketNo to modify the name of your value so you have a unique key to search for.
#!/usr/bin/perl -w
use strict;
=cut XHTML
<td><input type="checkbox" name="update" value="<TMPL_VAR NAME=TicketN
+o>" /></td>
<td><!-- TMPL_VAR NAME=TicketNo --></td>
<td><!-- TMPL_VAR NAME=Customer --></td>
<td><!-- TMPL_VAR NAME=UserName --></td>
....
<td><input type="text" name="detail_<TMPL_VAR NAME=TicketNo>" value="<
+TMPL_VAR NAME=AssignTo>" size="11" /></td>
=cut
...
my @update = $query->param('update');
foreach my $ticket_no (@update) {
my $assign_to = $query->param('detail_'.$ticket_no);
next unless defined $assign_to;
# do something with $ticket_no => $assign_to;
print qq|assign ticket number $ticket_no to $assign_to \n|;
}