Source: http://www.theweatherprediction.com/habyhints/190/

This led me to this calculator that will calculate the temperature given relative humidity and dew point - for example a dew point of 70°F and a relative humidity of 90% results in a temperature of 73.11°F. The web site for this calculator says the values are based on the August-Roche-Magnus approximation and gives the following equation to calculate temperature:

$T =243.04 \Large \frac{\frac{17.625\ TD}{243.04+TD}-\ln\left(\frac{RH}{100}\right)}{17.625+\ln\left(\frac{RH}{100}\right)- \frac{17.625\ TD}{243.04+TD}}$

Given the equation, I'm still having a hard time figuring out how the temperature is being calculated. Can somebody please explain how the temperature is being calculated in simple terms?

对于任何溶质溶剂，溶剂的温度越高，它能容纳的溶质就越多。这就是为什么热水比冷水能溶解更多的糖。或者，对于给定数量的糖，热水比冷水更快地溶解它。< / p >

The figure above says basically the same: Hotter air dissolves more water. Condensation happens when the amount of water in the air is more that the amount the air can actually hold. The dew point is the temperature at which condensation appears. Therefore, for a given relative humidity, the hotter the air, the higher is the dew point.

As you can see, in the Magnus approximation, the relationship is just a straight line, with a slope and constant changing for different values of the relative humidity.

I'll assign letters to each constant for simplicity, so that

$b=17.625$

and

$c=243.04$

With that, the dew point can be calculated as

$TD= \large c \LARGE \frac{\ln\left(\frac{RH}{100}\right)+\frac{b T}{c+T}}{b-\ln\frac{RH}{100}-\frac{b T}{c+T}}$

(see Calculating the dew point)

I won't do the algebra, but if you rearrange that formula so that $T$ is written as function of $TD$ and $RH$, you will go back to the formula you presented.