The fact that you can connect from machine A to machine B on port 22 doesn't imply that you'll be able to connect from B to A on port 22. After all, my desktop can connect to google.com
on port 80, but it definitely doesn't imply that the entire global array of google servers can connect to my desktop's apache instance.
Many things can get in the way: NAT, your site firewall, their site firewall, some firewall in between, to name but a few.
What you can do is use ssh to make a reverse tunnel back from the Sol 11 box to your desktop. You would do this by connection with
desktop% ssh solaris-11-server -R 2222:localhost:22
Then, when you're on the Sol11 box, and want to ssh to your home system, you connect to the Sol 11 box on port 2222 (which is just a random number, change it in the above and below commands if you need to), with
sol11% ssh localhost -p 2222