Sensitivity/specificity from PPV/NPV?

Is it possible to calculate the sensitivty and specificity from the PPV and NPV? I also know the total number in the population and the prevalence.

In more detail, I am looking at a medical diagnostic test. I know how many people were tested and I know how many had the disease (according to gold standard test), and I also know PPV and NPV. I want to know the sensitivity/specificity/tp/fp/tn/fn. Is it at all possible? If so, how?

I tried from equations to substitute different variables and landed at something but the results came out uninterpretable.

Help would be much apprecited. Thanks in advance // nyttpost
Yup, possible. Provide your number and plug em' into a classification table.
I'm sorry, but I'm not sure how such a classification table would be outlined?

This is the data I have:
Number of people taking new test: 1000
Number who had the disease according to gold standard test: 500
PPV of new test: 0,75
NPV of new test: 0,90

I want to calculate "backwards" to find sens/spec/tp/tn/fp/fn.