Apply Newton's second law to each block, assuming the system accelerates with magnitude $a$.

For block $m_1$ on the horizontal surface, the net force is the tension $T$:

$$T = m_1 a$$

For block $m_2$ along the incline, the net force is the sum of the applied force, tension, and the component of gravity parallel to the incline:

$$F - T - m_2 g \sin\theta = m_2 a$$

To find the tension, we can solve the system of two equations. From the first equation, express acceleration as $a = T/m_1$. Substitute this into the second equation to eliminate $a$:

$$F - T - m_2 g \sin\theta = m_2 \left(\frac{T}{m_1}\right)$$

Now, solve algebraically for $T$:

$$m_1 F - m_1 T - m_1 m_2 g \sin\theta = m_2 T$$ $$m_1 F - m_1 m_2 g \sin\theta = T(m_1 + m_2)$$ $$T = \frac{m_1(F - m_2 g \sin\theta)}{m_1 + m_2}$$