Let $I _ { n } = \int _ { 1 } ^ { e } x ^ { 19 } ( \log | x | ) ^ { n } d x$, where $n \in N$. If (20) $I _ { 10 } = \alpha I _ { 9 } + \beta I _ { 8 }$, for natural numbers $\alpha$ and $\beta$, then $\alpha - \beta$ equal to $\_\_\_\_$ .
Let $I _ { n } = \int _ { 1 } ^ { e } x ^ { 19 } ( \log | x | ) ^ { n } d x$, where $n \in N$. If (20) $I _ { 10 } = \alpha I _ { 9 } + \beta I _ { 8 }$, for natural numbers $\alpha$ and $\beta$, then $\alpha - \beta$ equal to $\_\_\_\_$ .