I have a 40 amp two pole breaker that powers 240 volts to a stovetop range and hood. The stovetop range requires 240 volts but the hood is only 120 Volts to power the fan and overhead light. If the 10-3 power coming in is 240, how do I get 120 (10-2) to the hood without losing 240 for the stove?

You should use a different feed for the hood. Do not use the 40A line from the range.
Also, 10/3 is too small for a 40A circuit. It should be #8cu at least.

Who ran this circuit?