So, this query seems to work for me, but I still am unsure why the thread_id and ticket_id are different and if it will always be an offset of 5. The offset of 5 seems arbitrary so I assume that there's some other way to link the two tables correctly.
SELECT number, ResponseTime, TicketCreateTime, round(time_to_sec(timediff(ResponseTime, TicketCreateTime))/60,2) AS FRMins
FROM
(SELECT TE.id, T.number, T.ticket_id, TE.thread_id, TE.pid, T.created AS TicketCreateTime, TE.created AS ResponseTime, TE.type, TE.staff_id
FROM ost_ticket T
INNER JOIN ost_thread_entry TE ON (T.ticket_id + 5) = TE.thread_id
WHERE T.created >= date('2019-05-31') AND TE.type = 'R' AND TE.id IN (SELECT min(id) FROM ost_thread_entry WHERE type = 'R' GROUP BY thread_id))AS FTRT_tbl