For those people like me- who do not use a cell phone- the issue of finding and using an "elite" number (in my case a SE number) is more challenging.

the obvious way is to find the number on the AC web site, after signing on to his/her account.
But under contacts (customer service) the generic AC reservations number still shows up (as mentioned in previous posts in this thread).

In the previous version of the AC web site, I could find under priority contacts find the SE toll free number.
In the current version of the AC/Aeroplan web site- under priority contacts as listed under Aeroplan (SE) core benefits- the number no longer displays.

So the only other non-app option is to find it on the back of one's Aeroplan card. But as of this year, the Aeroplan card is not automatically shipped to each Aeroplan member. One has to ask to get that card- which is what I did- and got it.

Failing the app , and failing the card - one can

a) call the general AC or Aeroplan number and ask for the "elite" tier number specific for that customer the next time

or
b) email online - via the customer service form that question