I believe negative is more commonly used but both seem to be okay. I've only really heard minus when someone's talking about the weather, like minus 10 degrees or 10 degrees below 0.
In the U.S., "minus" is much more commonly used when referring to temperature. We might also say, "It's eighteen degrees below zero."
Reed is correct, but to be fair, not many people (except scientists) in the US use degrees Celsius anyway!
Both "minus" and "negative" are acceptable ways of reading negative numbers. However, in the context of temperatures, a common and more concise way to read them is simply as "minus." Therefore, in this case, you can say the Earth's average temperature would be around minus eighteen or minus nineteen degrees Celsius.