scr879

I don't give much thought to the formulas. Just the concept of distribution. Think of the shape of the chi square distribution (like normal but lower limit is 0 and it is right skewed... hence it is not symmetrical)

Now for df = 10, significance level = .10, two tailed, you will have .05 in the left tail and .05 in the right tail.
.05 in the left tail means .95 in the right tail so lower limit is 3.94
.05 in the right tail is straight forward .05 with a value of 18.307 (as you suggested)