Solving for HR and FAR, given ACC and C
I tried to do the math and got stuck. I asked for help at math.se and didn't get any further. My thinking is that it is not possible to write down a nice simple answer even though it is two equations and two unknowns, since system is not linear. When faced with math I cannot do, sometimes it is easier to just bring out the MATLAB hammer:

function [HR, FAR] = findHRFAR(c, acc)
    ACC = @(HR, FAR)(HR+1-FAR)./2;
    C = @(HR, FAR)(norminv(HR)+norminv(FAR))./2;

    HR = fminbnd(@(HR)temp(HR, c, acc), 0, 1);
    [SSE, FAR] = temp(HR, c, acc);

    [HR, FAR, C(HR, FAR), ACC(HR, FAR), SSE]

    function [SSE, FAR] = temp(HR, c, acc)
        [FAR, SSE] = fminbnd(@(FAR)((c-C(HR, FAR)).^2)+...
            ((acc-ACC(HR, FAR)).^2), 0, 1);
    end
end


It runs pretty fast, but ... the nested bounded optimization is ugly, and there may be a more efficient way to find the answer. I also don't see any reason this could not be done in Octave, Python, or any similar type program of your choice.