The equivalent temperature $T_e$ of a parcel is the temperature it would have if all the water vapor of in the parcel were to condense and the liberated latent heat would heat the dry constituents of the parcel. Therefore,

$T_e = T + \Delta T$,

where $T$ is the parcels temperature before condensation and $\Delta T$ is the change in temperature due to the latent heat of condensation.

An expression for $\Delta T$ can be derived using

the change of energy due to a phase change :

$\Delta Q = m_v L$

where $m_v$ is the mass of water vapor and $L$ is the latent heat associated with condensation,

and

the change in temperature of dry air given by a change in energy and the heat capacity of dry air:

$\Delta Q = m_a C_p\Delta T$

where $m_a$ is the mass of dry air and $C_p$ is the heat capacity of dry air.

If all of the latent heat released by the change in phase warms the dry constituents of the parcel, then

$\Delta Q = \Delta Q \Rightarrow m_a C_p \Delta T = m_v L \Rightarrow \Delta T = \frac{L}{C_p}\frac{m_v}{m_a} = \frac{L}{C_p}W$

With this expression for $\Delta T$, we get the expression for $T_e$:

$T_e = T + \Delta T \Rightarrow \fbox{$T_e = T + \frac{L}{C_p}W$}$

Note : The mixing ratio $W$ must be in gm/gm or kg/kg.