From memory, and I'm getting old...
The ADT panel must be powered by a special power supply that will put the X10 signals onto the powerline.
The panel must be programmed to recognise that the X10 compatible power supply is installed.
The panel can then be programmed to send X10 ons and offs in response to various alarm events (setting, unsetting, alarms).
I looked into it a year or two ago, but the X10 compatible power supply was somewhere close to $80 so I didn't go much further.
The ADT panels are mostly modified Vista V15 or V20 series from Honeywell - you might find some info by looking for the programming instructions online. The main problem is that ADT probably locked you out of any programming functions.
Although some careful research may reveal the standard ADT programming code, you should probably be aware that unauthorised changes in the programming *may* report back to the monitoring system.
Good luck