Trough of Despair: Bracketed Words in Scriptures

I've read the Bible since I was a child, never really coming to grips with this "Greek thing" until recently.

I'm a simple layman, so I don't know Greek and probably never will study it....oh, maybe I'll break down and buy a Mounce "Greek for idiots" type book one day. The various translations (especially the literal ones) have been great eye openers for me.

Proof texting came naturally to me over the years growing up, but a few years ago, I first heard of this "exegesis" thing

Computer tools to allow me to see 8 or more translations side by side are wonderful...and yet at times frightening.

Maybe you've heard of the famous enthusiasm curve:

1 interest
2 enthusiasm
3 high enthusiasm
4 realization of the complexity
5 trough of despair
6 reality

Right now, I think I'm somewhere between phase 4 and 5 of my "digging as deep as possible" project.

Let's take an example of what boggles my mind. Looking at Romans 5:18 in ASV and literal, we see some phrases that were added to the English by the authors..phrases that are not in the Greek as far as I can tell with side-by-side comparison tools.

The KJV adds the same bracketed words as the ASV does. I've googled around and looked at numerous commentaries, but I can't for the life of me find any explanation of why these words were just thrown in there.

I was looking at this verse in context of studies on Arminianism versus Calvinism (so don't worry, I'm not trying to work some misguided Universalist angle)

It could be any bracketed words anywhere, I suppose. This was just a blatant example of words that just aren't to be found in the Greek, so I can't figure why it was tolearated that they were added to the English.

Now I haven't seen a side-by-side of English and the vulgate (and I can't read Latin either), so I don't know if maybe they were added there too.

Any help anyone can provide on this brackets issue in general would be appreciated.