# Elbow method gives very different number of clusters than Silhouette method in kmeans

I am trying to cluster tweets using k means algorithm. In order to find the best number of clusters I run the elbow method and the Silhouette method for 1 to 14 clusters. However, the elbow method gives 8 clusters and the Silhouette method gives 14 clusters which is the max number of clusters (So I suppose that if I check for more clusters the Silhouette score will improve more). The Silhouette output is this:

[(14, 0.01099081385755934), (13, 0.010913600577875339), (15, 0.010735258452729449), (12, 0.009972398884037042), (11, 0.009873906887295263), (10, 0.008924420881453054), (9, 0.00837275406765135), (8, 0.008038285782741293), (7, 0.007561470837121052), (6, 0.006995317289821658), (5, 0.006343859527220237), (4, 0.005040021066862907), (3, 0.004212974332611302), (2, 0.003538406316643856)]

where the first number is the number of clusters and the second is the Silhouette score. I use tfidfVectorizer to tranform the tweets into a tweets x documents matrix. Why is there such a big difference between the 2 methods outputs and which method should I trust?