I was about to ask this question and I believe I discovered the solution.
use notepad++ and use find in files function (a tab after hitting ctrl+f)
search for "hesk_notifyCustomer();" and comment all hesk_notifyCustomer code.
C:\wamp\www\admin\admin_reply_ticket.php (1 hit)
Line 261: hesk_notifyCustomer('new_reply_by_staff');
C:\wamp\www\admin\admin_submit_ticket.php (1 hit)
Line 259: // hesk_notifyCustomer();
C:\wamp\www\inc\email_functions.inc.php (2 hits)
Line 50: function hesk_notifyCustomer($email_template = 'new_ticket')
Line 69: } // END hesk_notifyCustomer()
C:\wamp\www\inc\pipe_functions.inc.php (1 hit)
Line 316: hesk_notifyCustomer();
C:\wamp\www\submit_ticket.php (1 hit)
disable customer email notifications
Moderator: mkoch227
Re: disable customer email notifications
Good find 

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Also browse for php hosting companies, read php books, find php resources and use webmaster tools