He probably avoided paying income taxes for much longer than that, otherwise he would have released some tax returns. We only know that he didn't pay income tax on the years that he had to submit to the New Jersey gambling commission, and the state tax returns for that one year show the nearly billion dollar loss that would have allowed him to reduce his taxes for 18 years. That billion dollar write off is most likely something different. Bill Kristol said it was probably "debt parking". Mark Cuban said that the donald's income at that time wasn't even large enough for the write off to be used for that even over 18 years. Since I'm not a billionaire or an accountant, I can't explain it, but that billion dollars might be something even more illegal than what people are assuming.
It may take me the rest of the day to get through the donald's deplorable list that @backformore posted above.