How to do a heat problem involving a change of state

The first question is calculate the final temperature if 15g of steam at 110C are passed into 250g of water at 10C contained in a 150g aluminum cup.

I've tried multiple times to figure it out and keep getting answers that are way off

The other question is: an aluminum calorimeter with a mass of 10g contained a piece of copper having a mass of 200g and 100g of water at 35C. What is the mass of ice at -20C that must be added to lower the temperature of the mixture to 15C?

I can't figure out this question either, any help would be really great thanks so much!
*C stands for degrees Celsius

You have to do it a piece at a time.
specific heat of water is 4.186 kJ/kgC
specific heat of ice is 2.06 kJ/kgC
specific heat of steam is 2.1 kJ/kgK
heat of fusion of ice is 334 kJ/kg
heat of vaporization of water is 2256 kJ/kg
specific heat Aluminum is 900 J/kgC

Heat to cool the steam to 100º
E1 = 2.1 kJ/kgK x 0.015 kg x (110–100)

heat to condense the steam
E2 = 2256 kJ/kg x 0.015 kg

heat to cool the water from 100 to final temp T
E3 = 4.186 kJ/kgC x 0.015 kg x (100–T)

heat to warm the second batch of water to final temp T
E4 = 4.186 kJ/kgC x 0.25 kg x (T–10)

heat to warm aluminum
E5 = 0.90 kJ/kgC x 0.150 kg x (T–10)

Now simplify the above and combine into
E1 + E2 + E3 = E4 + E5
and solve fot T