Assume Josh made X cupcakes; Alice made Y cupcakes; Tom made Z cupcakes.
Josh made 10 more cakes than Alice so, 
X = Y + 10 ---- 1st Eqn.
Alice made 8 more than Tom so, 
Y= Z+8 --- 2nd Eqn. 
Total cakes = 62 so, 
X+Y+Z = 62  ---- 3rd Eqn.
by solving three equations we get X= 30; Y= 20; Z=12.
So Tom made 12 cupcakes