We can rearrange and simplify to get:
#-2xsin(x-y)=y#
#d/dx[y]=d/dx[-2xsin(x-y)]#
#d/dx[y]=d/dx[-2x]sin(x-y)-2xd/dx[sin(x-y)]#
#d/dx[y]=-2sin(x-y)-2xd/dx[sin(x-y)]#
#d/dx[y]=-2sin(x-y)-2xcos(x-y)d/dx[x-y]#
#d/dx[y]=-2sin(x-y)-2xcos(x-y)(d/dx[x]-d/dx[y])#
#d/dx[y]=-2sin(x-y)-2xcos(x-y)(d/dx[x]-d/dx[y])#
Using the chqain rule we get that #d/dx=dy/dx*d/dy#
#dy/dxd/dy[y]=-2sin(x-y)-2xcos(x-y)(1-dy/dxd/dy[y])#
#dy/dx=-2sin(x-y)-2xcos(x-y)(1-dy/dx)#
#dy/dx=-2sin(x-y)-2xcos(x-y)+2xcos(x-y)dy/dx#
#dy/dx-2xcos(x-y)dy/dx=-2sin(x-y)-2xcos(x-y)#
#dy/dx[1-2xcos(x-y)]=-2sin(x-y)-2xcos(x-y)#
#dy/dx=-(2sin(x-y)+2xcos(x-y))/(1-2xcos(x-y))#