It is not possible to retrieve/restore a deleted ticket in HappyFox.
In order to find the delete log, you'll need to go to that particular ticket's URL (<your_happyfox_URL>/staff/ticket/<ticket_number>).
Say for example, your account is abcd.happyfox.com, and you deleted the ticket AB00001234; the ticket's URL you'd need to go to would be - abcd.happyfox.com/staff/ticket/1234.
The log provides the name of the staff who deleted the ticket, the time at which the ticket was deleted, Name and Email of the ticket raiser and the subject of the ticket.
As a workaround, though it may not ideally replace your deleted ticket, you can create a new ticket on behalf of the client, and use the text from the email notification of the deleted ticket, you would have previously received.