Reversing out IV from delta?

I think i’m going crazy, or I’ve just got more stupid. I have the delta, option premium, Future price, and days to maturity for a set of options on futures. BSM/Black76 allows us to get an analytical solution to solve for premium. I want to extract the IV implicit in the delta.

I can take the inverse of the normal distribution on the d1 term, but I can’t seem to re-arrange d1 to solve for sigma itself. Or have I missed a really obvious trick that means I have to use a newton-raphson type guess and verify method?

So far i have only got

d1 = (sigma^-1(lnF-lnK)) + 0.5sigma*T

Maybe this is high-school algebra (I must have missed that day), but how do i collect the sigma term?

It’s OK bros I got it.

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