No, it is not safe to cook a beef roast at 180 degrees Fahrenheit (82 degrees Celsius) for 18 hours in a slow cooker. The temperature and cooking time you have mentioned are within the "Danger Zone," which is the temperature range where bacteria can grow rapidly on food.
The safe temperature range for cooking beef and other meats is generally between 145 degrees Fahrenheit (63 degrees Celsius) for medium-rare and 160 degrees Fahrenheit (71 degrees Celsius) for medium doneness. The internal temperature of the roast should reach at least 145 degrees Fahrenheit to ensure that harmful bacteria like Salmonella and E. coli are killed.
Slow cookers are designed to cook food at low temperatures over a long period, but they should not be used at extremely low temperatures like 180 degrees Fahrenheit for such a prolonged time. It's essential to cook meats at temperatures high enough to quickly reach the safe internal temperature and avoid the risk of bacterial growth.
For slow-cooking a beef roast, it's best to set your slow cooker to a temperature range of 200-250 degrees Fahrenheit (93-121 degrees Celsius) and cook the roast for 8-10 hours until it reaches the desired doneness and internal temperature. Alternatively, you can also cook it in an oven at a temperature between 300-325 degrees Fahrenheit (149-163 degrees Celsius) for about 3-4 hours until it's cooked through.
Always use a meat thermometer to check the internal temperature of the beef roast to ensure it's safe to eat. If you're uncertain about the cooking temperature or time, it's better to err on the side of caution and follow a tested and safe recipe.