This becomes easy if you use Custom SQL to reshape your data. There are many forum posts describing how to do this, here's my advice, we do this type of counting a lot.

1. connect to your ticket data source and switch to Custom SQL
2. split each original ticket record into a start and end record using UNION ALL as depicted
3. use a running sum table calculation to show the total count open at any time

Depending on the density of your data there may be date periods in which no tickets were opened or closed. You could pad your data but we prefer to use delta bars instead of lines that may be discontinuous. Attached workbook is from Tableau 8.1.

You might also get inspiration from previous Q&As about open vs closed.

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Thanks for pointing out that because the data connection process is different in 8.2, the way to get to Custom SQL is different than depicted and varies depending on data source type. But once you get to Custom SQL, the SQL to duplicate the records and the Tableau view building process remain the same.

TThanks for this! Been struggling with the same problem!