If you are reading this you might be searching for a solution, saw my comment or just be browsing the internet. So here's the thing, I saw a Numberphile and was like "i gotta try that" https://www.youtube.com/watch?v=Y30VF3cSIYQ . I do recreational math, so you know.... i like a challenge. anyway here's the solution I came up with (I circled) the "magic step". Basically the realization is that the left and right sides are in the same form. and since I made "I" up I can choose it to be equal to B which forces the other side to be A which then of course dictates its value.
This was my 2nd attempt I spent a few minutes going down another path to see if i could turn it in to a quadratic and just get solutions... it was a mess so I went back and looked for well, what you see. Oh and above The J substitution isn't necessary. i was just doing it to see if anything made sense as a next step beyond the obvious. it didn't help you could remove it. I just didnt want to rewrite the work and i did it in ink so... there it stands.