a microcontroller will likely be easier
to get direction control of a DC motor you'll probably be wanting to use a full H-Bridge (even with a uC). There are chips which are suitable for powering DC motors of a few amp. Control inputs are direction, and run.
It's possible to implement the timing characteristics using a 556 IC (that's two 555's on a single chip) Wire the two "555s" up as monostables which trigger each other. then connect the output from the quicker monostable (set up to delay for 10s) to the H-bridge's run pin
http://en.wikipedia.org/wiki/555_timer_IC#Monostable
such a circuit might start oscillating on it's own but you might need to add a start button to get it going.
direction control...
connect the comparators output to the H-bridge's direction pin
connect the PV cells to each input of the comparator.
You may need to swap which pin connects to which PV cell or the wiring to the motor- as there the possibility you might wire the motor up so it runs in the wrong direction.
NB you do know when light is shone on their P-N junctions *all* semiconductor diodes will work as tiny PV cells? with a good CMOS comparator that doesn't draw much current you probably don't need to use "proper" solar cells for light detection. a pair of LEDs should be able to generate enough voltage difference to switch the comparator
Comparators chips are often wired as open collector. That means when output is low the short the output to ground. When output is high they aren't shorting the output to ground. As such you often need to add a pull resistor to get a voltage on the comparator's output pin
Hope that helps