To solve this, we first need to convert the mixed numbers to improper fractions.

10 5/14 = (14 * 10 + 5)/14 = 145/14

3 5/14 = (14 * 3 + 5)/14 = 47/14

Now, we can rewrite the expression:

145/14 - (47/14 + 29/34)

Next, we need to find a common denominator for the fractions inside the parentheses, which is 34:

145/14 - (47/14 + 29/34)
= 145/14 - (472/142 + 29/34)
= 145/14 - (94/28 + 29/34)
= 145/14 - (94/34 + 29/34)
= 145/14 - 123/34
= (14534 - 12314)/14*34
= (4930 - 1722)/476
= 3208/476
= 1604/238

Therefore, 10 5/14 - (3 5/14 + 29/34) = 1604/238