interface ConsumerE<T, E extends Exception> {
        void accept(T t) throws E;
    }

Note that Java 8 also includes specialized wrappers like RuntimeIOException. So it might be nice to extend your example:

    static <T, E extends Exception> Consumer<T> wrapped(
            Function<? super E, RuntimeException> wrapper,
            ConsumerE<T, E> consumer) {
        return (t) -> {
            try {
                consumer.accept(t);
            } catch (RuntimeException e) {
                throw e;
            } catch (Exception e) {
                throw wrapper.apply((E) e);
            }
        };
    }

    Consumer<String> printer = wrapped(RuntimeIOException::new, writer::write);