It can't be balanced because it is in fact sum of two reactions, each can be balanced separately:
2C2H5OH + 9I3- -> 18I- + CO2 + 3CHI3 + 9H+
2C2H5OH + 8I3- -> 15I- + HCOO- + 3CHI3 + 8H+
Now, you can add them side by side:
4C2H5OH + 17I3- -> 33I- + CO2 + HCOO- + 6CHI3 + 17H+
Technically this is a balanced reaction, but this approach doesn't yield unique equation, as any linear combination of these reactions will still look balanced, for example:
136C2H5OH + 595I3- -> 1173I- + 51CO2 + 17HCOO- + 204CHI3 + 595H+
but no real mixture will follow this stoichiometry.