Consider the car and trailer as a single system with total mass $M = m_1 + m_2$. The net external force on the system is the traction force minus the total resistance force.

Applying Newton's second law to the entire system:

$$F - f_1 - f_2 = (m_1 + m_2)a$$

Solving for the acceleration $a$:

$$a = \frac{F - f_1 - f_2}{m_1 + m_2}$$

To find the tension force $T$, we can isolate the trailer (mass $m_2$). The forces acting on the trailer are the tension $T$ pulling it forward and the resistance $f_2$ opposing its motion.

Applying Newton's second law to the trailer:

$$T - f_2 = m_2 a$$

Solving for $T$ and substituting the expression for $a$:

$$T = m_2 a + f_2 = m_2 \left( \frac{F - f_1 - f_2}{m_1 + m_2} \right) + f_2$$

Simplifying the expression for $T$:

$$T = \frac{m_2(F - f_1 - f_2) + f_2(m_1 + m_2)}{m_1 + m_2} = \frac{m_2 F - m_2 f_1 + m_1 f_2}{m_1 + m_2}$$