To answer this question, we need to start with the definitions of what "tone" and themes" actually are. So:
Tone is the general feeling of the text. It has more to do with the way in which the author intends for the reader to feel while reading the work. For instance, a story about a child playing with a puppy can have a light, happy tone, whereas a poem about the death of a loved one will have a dark or sad tone.
A theme is the main idea of a work, sometimes referred to as the "big idea." For example, a story could be about the loss of innocence through the experience of life's cruelties, or it could be that the best way to go through life is to keep a postitive outlook, even when it seems as though life is nothing but bad.
So, tone helps to develope the theme in that if you are reading a story in which the main idea centers around the concept that an individual will inevitably suffer a loss of the childish innocence that we so treasure because of the harsh cruelties of reality, the tone is going to be pretty dark and depressing to get that point across. Usually, unless you are reading a satirical work, the tone and the theme, though very separate elements, are usually a good match.
Tone helps develop theme because it demonstrates where the author’s focus lies and the author’s attitude, which reinforces the themes the author is trying to develop.
Tone is the author’s attitude toward a subject. The tone can be humorous, friendly, angry, or any other emotion. Tone helps establish the mood of the story, which is the emotion the reader should be getting with the reading.
Consider this example from Ray Bradbury’s short story “There Will Come Soft Rains.” This story depicts a lifeless automated house after its humans died in an apocalypse. Bradbury clearly intends for this to be a cautionary tale about relying on technology. Consider this quote:
The dog, once huge and fleshy, but now gone to bone and covered with sores, moved in and through the house, tracking mud. Behind it whirred angry mice, angry at having to pick up mud, angry at inconvenience.
We can really tell that the author is frustrated that the dog has died and the mice don’t care. He wants us to feel it. His tone is brusque and frustrated. The reader understands the theme even better, that technology can sometimes get out of control and the things that are supposed to help us can destroy us.
To answer this, first you have to understand to what the literary term "theme" refers. As stated above, the theme of a literary work is the message imparted by the writer. While the actual theme may be something unbiased, the author must have some opinion of the topic (or else he or she wouldn't be writing about it). A prime way for an author to express his or her views on the theme are through tone. This can include mere positive/negative opinions on the subject. However, it can also be more complex because tone in its various forms - emphatic, professional, harsh - can depict finer nuances of an author's approach to the topic. By correctly identifying the tone the author uses, readers gain further insight into the theme of a work.