解:由题意,得$AE = OA = BC = 10,$$OD = DE,$$AB = OC = 8$
折痕$AD$所在的直线是四边形$OAED$的对称轴
在$Rt\triangle ABE$中,$AE = 10,$$AB = 8$
根据勾股定理$BE=\sqrt {AE^2-AB^2}=\sqrt {10^2-8^2}=6$
∴$CE = 10 - 6 = 4,$则点$E$的坐标为$(4,$$8)$
在$Rt\triangle DCE$中,$DC^2+CE^2=DE^2$
又∵$DE = OD,$设$OD=x,$则$(8 - x)^2+4^2=x^2$
解得$x = 5,$∴点$D$的坐标为$(0,$$5)$