I was wondering what you are going to do after knowing the hydrogen bond energy.As far as I know there are no direct methods in Gromacs, same for hydrophobic interaction energies.
There is tool available, MDanalysis python package or try in YASARA which will give hydrogen bond energy at particular structure -not over time.
There is an indirect way. No of hydrogen bonds between solute and solvent can be found in gromacs. In a paper by berendsen et.al, they have mentioned that HB energy of one HB for a particular water model. for SPCE model it is -30 KJ/mol. Multiply this value with No.of hydrogen bonds you will get HB energy.