\[ \begin{align*} \text{Average age of 35 students} & = 14 \,years \\ \text{Sum of ages of 35 students} & = 14 \times 35 \\ & = 490 \\ \\\text{Average age of 35 students and 1 teacher} & = 15 \,years \\ \text{Sum of ages of 35 students and 1 teacher} & = 15 \times 36 \\ & = 540 \\ \\ \text{Age of the teacher} & = 540 - 490 \\ & = 50 \,years\end{align*} \]

Answer Age of the teacher \( \boxed{\color{red} 50\, years}\)

\[ \begin{align*} \text{Average marks of 10 students} & = 60 \\ \text{Sum of marks of 10 students} & = 60 \times 10 \\ & = 600 \\ \\\text{Average marks of 9 students} & = 59 \\ \text{Sum of marks of 9 students} & = 59 \times 9 \\ & = 531 \\ \\ \text{Highest mark} & = 600 - 531 \\ & = 69 \, Marks\end{align*} \]

Answer Highest mark \( \boxed{\color{red} 69 \, Marks}\)

\[ \begin{align*} \text{Let the 2 numbers be } & x \text{ and } y \\ \\ \text{Mean of 2 numbers} & = 10 \\ \frac{x + y}{2} & = 10 \\ \\ x + y & = 2\times 10 \\ x + y & = 20 \\ \\ \text{Difference between 2 numbers} &=0 \\ \\ x - y &=0 \\ x &=0 + y \\ x &= y \\x + y & = 20 \\ x + x & = 20 \\ 2x & = 20 \\ \\ x & = \frac{20}{2} \\ \\ x & = 10 \\ y & = 10 \\\end{align*} \]

Answer The numbers are \( \boxed{\color{red} 10 , 10}\)