To solve the expression \( \frac{1}{2} - \left( \frac{1}{3} + \frac{1}{10} \right) \), we need to follow these steps:

1. First, calculate the sum inside the parentheses:
\[ \frac{1}{3} + \frac{1}{10} \]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 3 and 10 is 30. Convert each fraction to have the denominator of 30:
\[ \frac{1}{3} = \frac{10}{30} \]
\[ \frac{1}{10} = \frac{3}{30} \]

Now add the fractions:
\[ \frac{10}{30} + \frac{3}{30} = \frac{10 + 3}{30} = \frac{13}{30} \]

2. Next, subtract this result from \( \frac{1}{2} \):
\[ \frac{1}{2} - \frac{13}{30} \]

Again, we need a common denominator. The LCM of 2 and 30 is 30. Convert \( \frac{1}{2} \) to have the denominator of 30:
\[ \frac{1}{2} = \frac{15}{30} \]

Now perform the subtraction:
\[ \frac{15}{30} - \frac{13}{30} = \frac{15 - 13}{30} = \frac{2}{30} \]

3. Simplify the fraction \( \frac{2}{30} \):
\[ \frac{2}{30} = \frac{1}{15} \]

So, the final result is:
\[ \frac{1}{15} \]