I don’t know where you read the statement “NADPH is... the main agent necessary for anabolic reactions”, but out of context it is very misleading, and it is difficult to envisage circumstances in which it would be helpful for students of metabolism.
Put simply, NAPH is only used in anabolic pathways which involve chemical reduction.
You ask for a suitable book, but the book I’m going to quote from (Berg et al., Biochemistry) would overwhelm you (and any other student — it is grossly overweight). However an old edition is available on-line, and by citing specific sections you can read what is relevant (and spare me breaking up my answer with pirated diagrams).
ATP and NADPH: energetic similarities and differences
ATP and NADPH can both be regarded as ‘energy-rich’ in the sense that they can undergo reactions that have a high negative change in Gibbs Free Energy (which is what determines whether a reaction proceeds) and that this can be linked to certain other reactions with a positive free-energy change — including, but not exclusively, those in biosynthesis — to drive an overall reaction. (Incidentally both these compounds are synthesized in reactions powered by solar energy during photosynthesis.) However the nature of this linkage or coupling to other reactions differs between NADPH and ATP, and this difference determines the roles that they can play.
The oxidation of NADPH to NADP+ has a standard redox potential of +0.32V , which is an effective a negative standard free-energy change, but it can only occur in conjunction with another redox ‘half-reaction’ with a redox potential that will result in an overall negative free-energy change. Berg et al., section 18.2.1, presents a calculation to show how NADH (essentially similar to NADPH in this respect) can reduce pyruvate to lactate. The key point is that this overall reaction is a chemical reduction, so that the ‘energy’ of NADPH is only of use in reductive synthesis.
The ‘energy’ of ATP (more properly its group transfer potential) is in fact the negative free energy of the hydrolysis of ATP to ADP (and orthophosphate), or to AMP (and pyrophosphate). If an enzyme can couple this reaction to another with positive free energy of hydrolysis then it can drive the second reaction. This important point is dealt with in Berg et al. section 14.1.3 and it is also worth reading the preceding section. ATP is not a reducing agent so is not limited to oxido-reduction reactions. (The hydrolysis of ATP can also be used to provide e.g. mechanical or electrical or light energy, which is why Berg et al refer to it in section 14.1.2 as “…the Universal Currency of Free Energy in Biological Systems”.) In synthetic processes ATP (or other nucleotide triphosphates derived from it) is often used in reactions forming bonds (C–C, peptide, glycosidic, phophodiester). In some of these cases the hydrolysis of the ATP is used to generate an activated form of the basic component, which allows it to form the bond in a subsequent reaction.
Example of a synthetic pathway using both NADPH and ATP
In Fatty acid synthesis NADPH is used for two reduction reactions — ketone to alcohol, unsaturated C=C to saturated C–C bond — whereas ATP hydrolysis is coupled to the formation of the C–C bond of the condensing unit, malonyl CoA. This is shown in Figure 22.22 of Berg et al..
Example of synthetic pathways using ATP but not NADPH
The synthesis of the peptide bonds of proteins requires condensation of the carboxylic acid group of one amino acid with the amino group of another. This is not a reductive process and NADPH is not involved. ATP hydrolysis ‘activates’ each amino acid by attaching it to the ribose of a transfer-RNA in a bond that has a high enough free energy of hydrolysis to ‘drive’ peptide bond formation to the growing polypeptide chain at the peptidyl transferase centre of the ribosome.
This is an area in which I am profoundly ignorant, but from Googling it would appear that the first phase of melanin synthesis is the conversion of tyrosine to DOPA and then to indoles. These reactions are oxidative (using molecular oxygen) rather than reductive, so do not use NADPH, and the bond formation is cyclization to form the pyrole ring. This seems to proceed without ATP — presumably it is energetically favourable overall. There is a Wikipedia entry for the key tyrosinase oxidation reaction.
I suppose the anabolic phase is the polymerization of the aromatic units to form the crosslinked polymeric structure of melanin. This appears to be poorly understood, but there is certainly no indication that NADPH is involved, and it would appear to depend on chemical features of the environment of the melanosome, rather than on ATP. (There is a recent short review in this area by VJ Hearing).
You mention the role of sunlight in this process. Although sunlight in itself can provide the energy for one stage of the synthesis of Vitamin D in the skin, this is a ring-splitting step. A direct role in the polymerization of melanin doesn’t seem to be suggested.