In this case, the nature of the problem and the solution are known. The builders have a complete drawing, all the tools, and the materials. All the difficulties are known and the methods to solve them are also known. Whether it is a small work shed, or a giant building, or even an airplane, all aspects of the problem have previously been worked out. .These can be very large problems but their beginning and end is defined and the steps to complete the tasks are all defined.
The artist knows what he wants to achieve, he has all the tools and the material, but he is not sure before he begins how to accomplish the end result he wants. Neither does anyone else know how to achieve the end result he wants. So the artist has to work out a new solution. So the problem is known, but the solution is not known and must be worked out. It could be the other way around. Perhaps the solution is known and readily available but the problem has not been defined. For example, we do not need to know how gravity works to be able to use the effects of gravity all the time.
Complicated problems happen when neither the definition of the problem nor the solution is known. How familiar this is! The baby is crying and has a fever. I don’t know what the problem is and I don’t know how to fix it. The usual approaches are 1) find an expert who can help (go to a doctor) or 2) make a “best guess” and monitor the symptoms of the problem to see if you guessed right. In this picture, you probably don't even know there is a problem. However, there is a highly venomous fish lying camouflaged just off to the right and down a little from centre. So you didn't know the problem, and you don't know how to solve the problem of warning someone else without getting stung.
I didn't really think you would have trouble figuring this one out - Global Warming! the really difficult problems that are so messy you don’t really know where to start, they are constantly changing and even if you start to correct one part of the problem you create problems somewhere else.They are called wicked problems because they are wickedly difficult to solve – and to solve the problem is really just finding ways to cope with it or to go around the problem or to find a series of compromises that seem to work out. Often it is not even really clear when the problem has reached the point where you really have done all you can constructively do.
To make matters worse, nobody is in charge of fixing global warming. If it goes too far, civil society as we know it will not be able to cope with the hundreds of millions of refugees, the drought, loss of infrastructure to keep civilization running and much more. We do not have a lot of time to fix it, even though the results are perhaps years away and will place our grandchildren in danger - or it could be much sooner, we are not certain of the timing. But we do know that there are only a few decades at most to bring global warming to a full stop to achieve a stable climate.