Exim is having problems sending messages to the latest SM 14. I'm not sure who to blame but we didn't have the problem until the latest version of SM 14.
To temporarily fix the problem edit your exim.conf and in the "Transports Configuration" section you'll have your "remote smtp" transport section. You need to add "hosts_avoid_tls=*" to that section. So it will look something like:
driver = smtp
interface = xxx.xxx.xxx.xxx (an IP Address if you use a specific interface)
This fixed the problem for our Exim server to send to SM 14 but this doesn't fix the millions of other Exim servers that are probably having the same problem sending to SM 14. You lose TLS on Exim, but at least you can communicate.
There's probably another way to accomplish this, but the issue remains that Exim and SM 14 don't get along very well. We're running Exim 4.86 and I've even re-compiled Exim and the exim.conf to default and the problem still exists unless you drop TLS for outbound transport.