Off the top of my head, since I don't have this problem right in front of me:
The current needed for the heater is simply 1 KW divided by 240 V. So that is:
1000 W / 240 V = 4.167 A
For the motor, you need to use the Motor Tables at the end of NEC Section 430 to find the FLC (full load current) needed to properly size the conductors. It should be Table 430.248 for 1-phase AC motors, off the top of my head. Look for 1-phase, 230 V, 10 HP in this table to find the required FLC. Off the top of my head, I believe it is 50 A.
Then still for the motor, you need to multiply this motor FLC by 125% as per NEC Section 430.22 and 430.24.
50 A x 1.25 = 62.5 A
So the total amps required for both the motor and the heater is:
62.5 A + 4.167 A = 66.667 A
Then you need to go to NEC Table 310.15(B)(16) (if I remember right off the top of my head) to find the correct minimum size conductor that has an ampacity greater than or equal to this total current (66.667 A).
I will double-check my work I did for this problem when I have the time.