Hi and thanks for your question,
the commonest disease that causes an increase in white blood cell
level with a decrease in hemoglobin
levels is a type of blood malignancy generally called leukaemias. Leukamias are cancers of the white blood cells. Other conditions like severe infections could also cause an increase in white blood cells too and anemia.
Autoimmune diseases lie systematic lupus erythematosus
in some rare cases could present itself in the same way.
A definitive diagnosis is made when all the other possibilities have been excluded. A bone marrow
aspirate, an exam done wit the bone marrow to confirm diagnosis is usually most appropriate.
I suggest patient should visit his hematologist
or internist for a proper clinical exams and appropriate exams. Exam results are key issues in determining the diagnosis and proposing an appropriate treatment plan.
Thanks and hope this helps,