In my opinion, it is impossible.

Accuracy = 1 - mean(abs( (X_Calc - X_Meas)/X_Meas) ) and

 MAE = mean(abs(X_Calc - X_Meas)) .

But mean(A/B) =/= mean(A)/mean(B)

If the error bar is Gaussian, I think there is a relation between MAE and MSE

MAE = sqrt(2/pi)*sqrt(MSE)

Holds true when bias is zero or when errors follow normal distribution with zero mean, and constant variance