I'm on the same side with those pointing hard at the Head Gasket failure as the culprit. But the story of the "White Smoke" can get more complicated to repair and as such more expensive as time goes by. Symptomatically its a fairly easy thing to diagnose: Plumes of White Smoke intermittently appearing in the exhaust stream. However, two investigations should be made to nail down how much time you have before the engine declines and finally spins crankshaft bearings and seizes up, Here are the reasons why:
Symptom #1 PEG -Poly-Ethylene-Glycol in the Oil Stream:
Besides being a sweet tasting fluid that stray dogs find delicious enough to drink if they locate any pans of the stuff sitting around (It paralyzes and kills them afterwards)... PEG is EXTREMELY ACIDIC. If Anti--Freeze-Coolant is allowed to enter the main supply of oil... as it is pumped and circulated through the engine... it reacts with the Babbitt Coatings on the surfaces of the Crankshaft, Connecting Rods and Camshaft Bearings...and dissolves those surfaces by chemical corrosion. The rotating assembly will eventually over-heat from friction and seize up and snag on the bearings, causing them to spin in place in the block, effectively lunching the motor. This condition of AF-OIL can be determined by examining your Engine Oil for what looks like Chocolate Milk instead of the expected amber green, healthy Motor Oil.
If you can see the Brown Mung on your dipstick...catastrophic engine failure is coming. The engine can be salvaged by a re-build involving flushing out all that crap and essentially install new bearings everywhere inside the engine. If you continue to drive with the Chocolate Milk in the Oil Pan, since the gooey liquid has no lubricating properties... therefore, the interior engine components have no protective thin film of oil separating stationary metal areas from metal rotating in the moving parts under normal Oil Pressure. The other bad feature of this Chocolate Milk Mung ...is that it is of a consistency that is much like pudding and as such, It makes it impossible for the Oil Pump Pick-Up Tube to suck in anything and after the pump cavitates... The entire engine is without any oil lubrication. The Metal to Metal contact in any circumstance can cause 50,000 miles of engine wear in a matter of days.
https://s-media-cache-ak0.pinimg.com/originals/6f/c4/c8/6fc4c8dce904972e47c5bd696c945307.jpg
Symptom #2: Oil Droplets floating in the Radiator just under the cap...
The presence of Engine Oil in the Anti-Freeze is an indication in the best conditions as a Blown Head Gasket adjacent proximal Oil and Water Passages shared between the Engine Block and the Heads (probably not the case in your motor), The worst case scenario is that for one reason or another, there is a crack in one or more cylinders in the engine block allowing oil to push through and enter the coolant passages. If the engine is to be saved, the motor needs dis-assembly and new bearings throughout before it is damaged beyond any hope of repair from continued use.
http://www.team-bhp.com/forum/technical-stuff/134621-do-i-need-change-head-gasket-3.html