To determine the sign of the product of two negative numbers, we apply the rule that states that the product of two negative numbers is positive.
Given the numbers:
- \( -10.4 \) (negative)
- \( -78.2 \) (negative)
Calculating the product:
\[ -10.4 \times -78.2 \]
Since both numbers are negative, their product will be positive.
Hence, the sign of the product is:
\(+\)
So the answer is \(\text{+}\).