The processes of evaporation and transpiration actually depend on a wide range of factors, including all components of the water and energy balances at the surface, as well as wind, surface roughness, topography, plant and soil properties, to mention some of the most important ones. You may want to consult
https://en.wikipedia.org/wiki/Evapotranspiration
and
http://www.fao.org/docrep/X0490E/x0490e04.htm
to get started. Next, you must realize that the fewer inputs you will allow into your estimation, the less reliable the result. So your question will only make sense if you also state what is your accuracy requirement: If you don't have one, then any formula (even a random number generator) will do. On the other hand, if you do need a minimum level of accuracy, then you should also be prepared to require more useful inputs than precipitation and maximum temperature... and at least verify whether a simpler method is "good enough for your purpose", compared to a more elaborate one.
In practice, the formula you will use may depend on the availability of inputs, on your computing resources and skills, as well as on the accuracy needs of your application. Beware of conclusions based on poor input data or simplistic models.
If you want to calculate potential evapotranspiratin, there are a lot of different method, but you don't need precipitation in no one of them. you could estimate ET using temperature data, but you need both minimum and maximum temperature data, there for you could easily use FAO irrigation and drainage paper 56 to estimate PET from max and min temperature data.
Hi Salem - Certainly there are several factors to consider in estimating evap, as Michel points out.
I only have a brief addition to this thread: as you requested, here is a "simple" method of evap estimation - introduced, described, and applied in Renner et al. (2016) - which assumes max convective power and no surface water limitations. With this, one can estimate evap with only absorbed solar radiation and surface temperature.
Cheers - John
Article Dominant controls of transpiration along a hillslope transec...
Hemon's equation (1960) just uses air temperature and has been found to correlate well with the FAO-PM equation, and is widely used when there is no other met data available. You can also access MODIS-16 global datasets for 2000-2014, that's at 1 SQ KM resolution; this needs a GIS for viewing the raster files.