Approaching from the minor road
You need to adapt the rules you learned about emerging from a minor road at a T junction. Instead of just checking to right and left in the sequence right-left-right, you should cover the road ahead.
This gives you a new sequence of checks: right-ahead-left-ahead-right. This simple sequence is the minimum you should do. As always, treat the junction with caution, and only emerge when it is safe to do so.
Approaching from the major road
Although you have priority, you must still look out for drivers coming from side roads. As you approach the crossroads, check your mirrors, ease your foot off the accelerator, and glance into the side roads to left and right. Do not miss out this procedure.
If you follow it every time, you should be able to react safely to anything unexpected.