Make this chart:

              Distance   Rate  Time
Slower train
Faster train

Let the slower train's rate be x.  Then the faster train's rate is x+10.
Fill this in and the time for each is 4 hours, so fill that in too:


              Distance   Rate  Time
Slower train              x      4  
Faster train             x+10    4

Use distance = rate·time to fill in the distances:

              Distance    Rate  Time
Slower train     4x        x      4  
Faster train   4(x+10)    x+10    4

The distance must total the 360 miles they were initially apart, so

   4x + 4(x+10) = 360 

Solve and get x = 40 mph 

So the slower train was going x=40 mph and the faster train was
going x+10 = 40+10 or 50 mph.

In 4 hours the slower train went 160 miles and the faster train went
200 miles and their total distance in opposite directions toward the
point at which they met is the total 160+200=360 miles they were apart originally.  So it checks.

Edwin