No you'll have to buy a new tile. Sorry couldn't resist it.
Self tap screws about 1" long x 1/8" A tube of external mastic and mastic gun, and aluminium sheet B & Q does all if of course in UK.
sheet of aluminium over the damage allow at least 2" overlap all round drill 3/16" holes one on each corner 1/2" in from each side mark out even distance two holes between along each side again 1/2" in
Mastic around the edge that will be in contact with the roof then diagonally strip of mastic across from each corner to form a cross, press it down on the damage area and drill 1/16" hole in to roof through one hole check the screw will go in tight, ok then drill out and fix the rest screw down one edge and alternate along each side to other edge so it seats even allow plenty mastic to Ouse out the edges wipe with damp cloth to tidy edge mastic strip.
If its a fibre glass roof then use fibreglass repair kit.
But personally I would use the first method I've known fibre glass repairs to come adrift with movement.
Bob UK, March 2014