I've seen almost all of my favourite artists over the years, but this is one guy I missed out on. I'm a big fan of his stuff, from his work with the Raspberries through his solo career. The problem is the guy just didn't play many live shows. Setlist.com shows him as playing one show in Toronto on December 1, 1977, at Maple Leaf Gardens. Billy Joel was there that night so Carmen would have opened, but other sources show Elliot Murphy as the opener. 

Lorne wrote:

By the time of that Maple Leaf Gardens show, Eric Carmen had reached the Billboard top 40 four times as a solo artist from 1976 to 1977 along with four times with the Raspberries prior to that -- and this included reaching #2 with "All By Myself" and #5 with "Go All The Way". On the other hand, Billy Joel had only reached the top 40 twice, and this had been about three years before -- and despite how well-known "Piano Man" has become over the years, it only reached #25 when it came out. Over the course of the following year Joel would certainly become the bigger act, but in December 1977 I would think that Carmen would have been the headliner.

Could be, but  I guess the question remains was Carmen even at the Gardens on Dec. 1, 1977? I certainly would have gone  if that was the case. By all accounts Joel played the Gardens as part of his The Stranger tour on Dec. 1, but who knows who opened (or closed) the show. Joel and Carmen were to play another show in Philadelphia five days later but I read on one site where Carmen backed out and was replaced by Walter Murphy (!).
 

Lorne wrote:

Before I posted yesterday, I had wanted to look into this via the Canadian Newsstream database, but couldn't access it at the time because my Toronto library card had expired. I was able to access it today, and the only result I obtained was from a listing of upcoming shows in The Globe and Mail on Nov. 30, 1977, written by Paul McGrath.

BILLY JOEL Mr. Piano Man likes writing about the faces in the barroom mirror. He also likes his piano. He's at Maple Leaf Gardens with Eric Carmen tomorrow night.

So it does look like Joel had already become big enough to be either the headliner or co-headliner for this show, although I'm not sure if this writer was that impressed by him. However, it seems that there was no review of the show in either the Globe or the Toronto Star, which is also part of this database.

Good detective work. One other thing I recall from the time is that Joel's album The Stranger, made a pretty big splash when it came out and songs like the title track and Movin' Out (Anthony's Song) got a lot of traction on FM stations. Carmen's Boats Against The Current was a relative disappointment in comparison, and maybe that's why he possibly "bailed' from the shows in Toronto and Philly.