Your question shows up in the right moment for me, when I was just looking for a good opportunity to explain this topic in this community.
The right sentence is "El hijo del Sol soy yo". The reason why this causes a lot of confusion in non-Spanish speakers resides on the fact that Spanish language has two different verbs (Ser/Estar) for what all other main European languages (such as English, French, German or Italian, just to mention some of them) have only one verb (to be in English, être in French, sein in German and essere in Italian).
Therefore, there is a distinction on when and how to use each of these two verbs even though it may translate into the same verb in your native language.
First of all you have to understand the verb itself:
Ser: Is used to express an intrinsic or acquired characteristic of yourself or the subject of your speech. It is something that is long lasting and that cannot change very easily or at all.
for example:
Yo soy Mexicano - I'm Mexican
Yo soy moreno - I'm a brunet
Luke, yo soy tu padre... - Luke, I am your father
Yo soy ingeniero - I'm an Engineer
Estar: Is used to express a state or temporary characteristic. The duration of this temporary characteristic can be tricky to explain but usually is of some few minutes, hours, days, weeks or months.
Yo estoy enfermo - I'm sick/ill
Yo estoy estudiando Español - I'm studying Spanish
Yo estoy cansado - I'm tired
Yo estoy comiendo una manzana - I'm eating an apple
It is also used to express when you are at a specific location.
Yo estoy en Canadá - I'm in Canada
Yo estoy en el hospital - I'm at the hospital
Yo estoy en mi casa - I'm at home
Yo estoy en el carro - I'm in the car
Once that you understand this, you can avoid awkward moments when you say:
Yo soy (un) enfermo - I'm insane
while you wanted to say:
Yo estoy enfermo - I'm sick/ill
Just as an additional comment, depending on the context, style and actually what you are writing or saying, to say "El hijo del Sol soy yo" or "Yo soy el hijo del Sol", are equally correct but then, once again, it all depends on what message you are trying to convey. "Yo soy el hijo del Sol" is a statement, while "el hijo del Sol soy yo" emphasizes the same statement giving it a more dramatical twist.