If you had a table containing only the first call details and another table containing only those of the second call you'd be able to join them, right? Then the two times would be in separate columns. You don't have to copy data or split the table to achieve this. It can be done logically by referencing the table twice in the query and using a self-join.
AVG(second_call.time_of_call - first_call.time_of_call)
from TheTable as first_call
inner join TheTable as second_call
on first_call.customer_id = second_call.customer_id
where first_call.call_attempt = 1
and second_call.call_attempt = 2;
Logically I split the table into two, one called first_call and one called second_call. The former only contains rows for call_attempt 1 and the latter for call attempt 2. This is enforced in the WHERE clause. I'm assuming each customer will only ever have one row for each call attempt number.
Then I join these tables on the customer_id. I use an inner join so only customers that have both first second calls will be processed. It would be a good idea to profile the data to see how this affects the quality of the calculation.
You'll likely want to change the subtraction inside the AVG() to get the format you need.
If run-time performance is critical it may be more run-time efficient to write this using window functions rather than a self-join, depending on what indexes exist and the cardinalities.