This theme reads its colors from your ~/.Xresources file so that you can
easily keep your emacs theme in sync with your xterm and other X applications.
This includes edits specifically for using with pywal generated colors.
Here you can see xterm and emacs, both configured with the .Xresources version of solarized.
Configure your theme in your ~/.Xresources like
*foreground: #000000
*background: #FFFFFF
*color0: #111111
! ...
*color15: #FFFFFF
You can also set colors specifically for emacs like
emacs*background: #123456
although this defies the whole purpose of this theme.
Remember that an X application gets its resources at startup. So to make changes
in your ~/.Xresources apply to your emacs, you have to reload the resource
configuration with xrdb ~/.Xresources and then restart emacs.