This is a shortcoming of Cathay's system - if you book a revenue ticket on their website none of the confirmation emails shows the ticket number (which starts 160...). If you book through their phone reservations line then the email confirmation you receive does include the ticket number. I have often worried about this, although so far I have not had a problem.

The place the ticket number does sometimes appear for tickets booked on the website is on your credit card statement where it will say "Cathay Pacific Airways 160xxxxxxxxxx". If it shows 160+10digits then that is the ticket number.