The inverse operation to GeoDisplacement is GeoDestination, so we can construct an inverse projection using it:
polar[{x_, y_}] := GeoDisplacement[{Sqrt[x^2 + y^2], ArcTan[y, x]/Degree}];
InverseEAE[coords_, c_] := GeoDestination[c, polar[coords]];
Now you can do:
In[]:= EAE[Here, GeoPosition[{0, 0}]]
Out[]= {-7.55175*10^6, 6.34236*10^6}
In[]:= InverseEAE[%, GeoPosition[{0, 0}]] == Here
Out[]= True
Jose.
