Outdoor and return air cross inside the core, exchanging heat and moisture through thin plates. Outdoor air is coloured by temperature (hot = red / cold = blue) and becomes supply air after the core.
$$T_{sa}=T_{oa}+\varepsilon_s\,(T_{ra}-T_{oa}), \qquad w_{sa}=w_{oa}+\varepsilon_L\,(w_{ra}-w_{oa})$$
Supply-air temperature T_sa and humidity ratio w_sa after the ERV. εs: sensible effectiveness, εL: latent effectiveness. At effectiveness 1 the supply air equals the indoor condition; at 0 it equals the outdoor air.
$$Q=\dot m\,c_p\,\Delta T+\dot m\,h_{fg}\,\Delta w,\qquad \dot m=\rho\,V$$
Recovered heat Q is the sum of a sensible term (temperature difference ΔT) and a latent term (humidity-ratio difference Δw). m-dot is the mass flow rate, ρ the air density (1.2 kg/m³), cp the specific heat (1005 J/kgK), hfg the latent heat of vapourisation (2.5×10⁶ J/kg).
$$w=\frac{0.622\,p_v}{P-p_v},\qquad p_v=\frac{RH}{100}\,p_{sat},\qquad p_{sat}=611.2\,e^{\frac{17.62\,T}{243.12+T}}$$
Humidity ratio w (moisture content of moist air) from the Magnus equation. pv: vapour pressure, psat: saturation pressure, P: atmospheric pressure (101325 Pa). Sensible heat handles temperature, latent heat handles moisture.