The second one is definitely better but it's still a bit incorrect because a problem cannot be an example of "knowledge". Knowledge can help you solve a problem but the problem itself is not knowledge. Generally your use of "knowledge" is a bit strange because "knowledge" is a very general term, perhaps equivalent to "the sum total of everything that you know". It's not used very often in this sort of context because it's very vague.
To describe the state of having a lot of knowledge about a specific area or subject, it would be better to use the word "expertise", or perhaps "experience" or "ability", and you should be careful to distinguish this from information, which someone might also need to solve the problem, regardless of how much experience they have.
It's not clear, in the first sentence, whether you mean expertise or information, but from the context of the second sentence it looks like you mean expertise/experience.
Perhaps you could say:
In order to obtain a more accurate result, additional problem-solving ability is required. One example of this would be the ability to solve a problem that involves finding anomalies with different parameters from those of the surrounding material.
EDIT: if you're talking about information, you could say
In order to obtain a more accurate result, additional information is required. This information could, for example, allow us to solve a problem that involves finding anomalies with different parameters from those of the surrounding material.