$\begin{align}  & \text{Let the seventh number be }x \\ & \text{The sum of the six numbers will be  }2+4+8+14+16+18=62 \\ & \text{The mean of the seven number is }10 \\ & \therefore \bar{x}=\frac{62+x}{7}=10 \\ & 62+x=70 \\ & x=8 \\ & \text{The mode is 8} \\\end{align}$