Exception coming out of close() in try-with-resource

I was reading about the try-with-resource in JDK7 and while I was thinking of upgrading my application to run with JDK7 I faced this problem..

When using a BufferedReader for example the write throws IOException and the close throws IOException.. in the catch block I am concerned in the IOException thrown by the write.. but I wouldn't care much about the one thrown by the close..

Same problem with database connections.. and any other resource..

As an example I've created an auto closeable resource:

public class AutoCloseableExample implements AutoCloseable {

    public AutoCloseableExample() throws IOException{
        throw new IOException();
    }

    @Override
    public void close() throws IOException {
        throw new IOException("An Exception During Close");
    }

}

Now when using it:

public class AutoCloseTest {

    public static void main(String[] args) throws Exception {
        try (AutoCloseableExample example = new AutoCloseableExample()) {
            System.out.println(example);

            throw new IOException("An Exception During Read");
        } catch (Exception x) {
            System.out.println(x.getMessage());
        } 
    }

}

how can I distinguish between such exceptions without having to create wrappers for classes such as BufferedReader?

Most of cases I put the resource close in a try/catch inside the finally block without caring much about handling it.